The commutator width of some relatively free lie algebras and nilpotent groups

Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian n...
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Autor*in:	Roman′kov, V. A. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	free (solvable metabelian nilpotent metabelian nilpotent) Lie algebra metabelian nilpotent) Lie ring free (ℚ-power nilpotent metabelian nilpotent) group commutator width elementary equivalence

Übergeordnetes Werk:	Enthalten in: Siberian mathematical journal - New York, NY [u.a.] : Consultants Bureau, 1966, 57(2016), 4 vom: Juli, Seite 679-695
Übergeordnetes Werk:	volume:57 ; year:2016 ; number:4 ; month:07 ; pages:679-695

Links:	Volltext

DOI / URN:	10.1134/S0037446616040108

Katalog-ID:	SPR017690137

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245	1	4	\|a The commutator width of some relatively free lie algebras and nilpotent groups
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520			\|a Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank.
650		4	\|a free (solvable \|7 (dpeaa)DE-He213
650		4	\|a metabelian \|7 (dpeaa)DE-He213
650		4	\|a nilpotent \|7 (dpeaa)DE-He213
650		4	\|a metabelian nilpotent) Lie algebra \|7 (dpeaa)DE-He213
650		4	\|a free (solvable \|7 (dpeaa)DE-He213
650		4	\|a metabelian \|7 (dpeaa)DE-He213
650		4	\|a nilpotent \|7 (dpeaa)DE-He213
650		4	\|a metabelian nilpotent) Lie ring \|7 (dpeaa)DE-He213
650		4	\|a free (ℚ-power nilpotent \|7 (dpeaa)DE-He213
650		4	\|a metabelian \|7 (dpeaa)DE-He213
650		4	\|a nilpotent \|7 (dpeaa)DE-He213
650		4	\|a metabelian nilpotent) group \|7 (dpeaa)DE-He213
650		4	\|a commutator width \|7 (dpeaa)DE-He213
650		4	\|a elementary equivalence \|7 (dpeaa)DE-He213
773	0	8	\|i Enthalten in \|t Siberian mathematical journal \|d New York, NY [u.a.] : Consultants Bureau, 1966 \|g 57(2016), 4 vom: Juli, Seite 679-695 \|w (DE-627)325572348 \|w (DE-600)2037555-4 \|x 1573-9260 \|7 nnns
773	1	8	\|g volume:57 \|g year:2016 \|g number:4 \|g month:07 \|g pages:679-695
856	4	0	\|u https://dx.doi.org/10.1134/S0037446616040108 \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
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912			\|a GBV_ILN_2522
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912			\|a GBV_ILN_4037
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912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
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936	b	k	\|a 31.00 \|q ASE
951			\|a AR
952			\|d 57 \|j 2016 \|e 4 \|c 07 \|h 679-695

Indexfelder

author_variant	v a r va var
matchkey_str	article:15739260:2016----::hcmuaowdhfoeeaieyreiagba
hierarchy_sort_str	2016
bklnumber	31.00
publishDate	2016
allfields	10.1134/S0037446616040108 doi (DE-627)SPR017690137 (SPR)S0037446616040108-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Roman′kov, V. A. verfasserin aut The commutator width of some relatively free lie algebras and nilpotent groups 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank. free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie algebra (dpeaa)DE-He213 free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie ring (dpeaa)DE-He213 free (ℚ-power nilpotent (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) group (dpeaa)DE-He213 commutator width (dpeaa)DE-He213 elementary equivalence (dpeaa)DE-He213 Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 57(2016), 4 vom: Juli, Seite 679-695 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:57 year:2016 number:4 month:07 pages:679-695 https://dx.doi.org/10.1134/S0037446616040108 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 57 2016 4 07 679-695
spelling	10.1134/S0037446616040108 doi (DE-627)SPR017690137 (SPR)S0037446616040108-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Roman′kov, V. A. verfasserin aut The commutator width of some relatively free lie algebras and nilpotent groups 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank. free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie algebra (dpeaa)DE-He213 free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie ring (dpeaa)DE-He213 free (ℚ-power nilpotent (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) group (dpeaa)DE-He213 commutator width (dpeaa)DE-He213 elementary equivalence (dpeaa)DE-He213 Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 57(2016), 4 vom: Juli, Seite 679-695 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:57 year:2016 number:4 month:07 pages:679-695 https://dx.doi.org/10.1134/S0037446616040108 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 57 2016 4 07 679-695
allfields_unstemmed	10.1134/S0037446616040108 doi (DE-627)SPR017690137 (SPR)S0037446616040108-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Roman′kov, V. A. verfasserin aut The commutator width of some relatively free lie algebras and nilpotent groups 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank. free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie algebra (dpeaa)DE-He213 free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie ring (dpeaa)DE-He213 free (ℚ-power nilpotent (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) group (dpeaa)DE-He213 commutator width (dpeaa)DE-He213 elementary equivalence (dpeaa)DE-He213 Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 57(2016), 4 vom: Juli, Seite 679-695 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:57 year:2016 number:4 month:07 pages:679-695 https://dx.doi.org/10.1134/S0037446616040108 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 57 2016 4 07 679-695
allfieldsGer	10.1134/S0037446616040108 doi (DE-627)SPR017690137 (SPR)S0037446616040108-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Roman′kov, V. A. verfasserin aut The commutator width of some relatively free lie algebras and nilpotent groups 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank. free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie algebra (dpeaa)DE-He213 free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie ring (dpeaa)DE-He213 free (ℚ-power nilpotent (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) group (dpeaa)DE-He213 commutator width (dpeaa)DE-He213 elementary equivalence (dpeaa)DE-He213 Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 57(2016), 4 vom: Juli, Seite 679-695 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:57 year:2016 number:4 month:07 pages:679-695 https://dx.doi.org/10.1134/S0037446616040108 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 57 2016 4 07 679-695
allfieldsSound	10.1134/S0037446616040108 doi (DE-627)SPR017690137 (SPR)S0037446616040108-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Roman′kov, V. A. verfasserin aut The commutator width of some relatively free lie algebras and nilpotent groups 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank. free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie algebra (dpeaa)DE-He213 free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie ring (dpeaa)DE-He213 free (ℚ-power nilpotent (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) group (dpeaa)DE-He213 commutator width (dpeaa)DE-He213 elementary equivalence (dpeaa)DE-He213 Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 57(2016), 4 vom: Juli, Seite 679-695 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:57 year:2016 number:4 month:07 pages:679-695 https://dx.doi.org/10.1134/S0037446616040108 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 57 2016 4 07 679-695
language	English
source	Enthalten in Siberian mathematical journal 57(2016), 4 vom: Juli, Seite 679-695 volume:57 year:2016 number:4 month:07 pages:679-695
sourceStr	Enthalten in Siberian mathematical journal 57(2016), 4 vom: Juli, Seite 679-695 volume:57 year:2016 number:4 month:07 pages:679-695
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	free (solvable metabelian nilpotent metabelian nilpotent) Lie algebra metabelian nilpotent) Lie ring free (ℚ-power nilpotent metabelian nilpotent) group commutator width elementary equivalence
dewey-raw	510
isfreeaccess_bool	false
container_title	Siberian mathematical journal
authorswithroles_txt_mv	Roman′kov, V. A. @@aut@@
publishDateDaySort_date	2016-07-01T00:00:00Z
hierarchy_top_id	325572348
dewey-sort	3510
id	SPR017690137
language_de	englisch
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author	Roman′kov, V. A.
spellingShingle	Roman′kov, V. A. ddc 510 bkl 31.00 misc free (solvable misc metabelian misc nilpotent misc metabelian nilpotent) Lie algebra misc metabelian nilpotent) Lie ring misc free (ℚ-power nilpotent misc metabelian nilpotent) group misc commutator width misc elementary equivalence The commutator width of some relatively free lie algebras and nilpotent groups
authorStr	Roman′kov, V. A.
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topic_title	510 ASE 31.00 bkl The commutator width of some relatively free lie algebras and nilpotent groups free (solvable (dpeaa)DE-He213 metabelian (dpeaa)DE-He213 nilpotent (dpeaa)DE-He213 metabelian nilpotent) Lie algebra (dpeaa)DE-He213 metabelian nilpotent) Lie ring (dpeaa)DE-He213 free (ℚ-power nilpotent (dpeaa)DE-He213 metabelian nilpotent) group (dpeaa)DE-He213 commutator width (dpeaa)DE-He213 elementary equivalence (dpeaa)DE-He213
topic	ddc 510 bkl 31.00 misc free (solvable misc metabelian misc nilpotent misc metabelian nilpotent) Lie algebra misc metabelian nilpotent) Lie ring misc free (ℚ-power nilpotent misc metabelian nilpotent) group misc commutator width misc elementary equivalence
topic_unstemmed	ddc 510 bkl 31.00 misc free (solvable misc metabelian misc nilpotent misc metabelian nilpotent) Lie algebra misc metabelian nilpotent) Lie ring misc free (ℚ-power nilpotent misc metabelian nilpotent) group misc commutator width misc elementary equivalence
topic_browse	ddc 510 bkl 31.00 misc free (solvable misc metabelian misc nilpotent misc metabelian nilpotent) Lie algebra misc metabelian nilpotent) Lie ring misc free (ℚ-power nilpotent misc metabelian nilpotent) group misc commutator width misc elementary equivalence
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title	The commutator width of some relatively free lie algebras and nilpotent groups
ctrlnum	(DE-627)SPR017690137 (SPR)S0037446616040108-e
title_full	The commutator width of some relatively free lie algebras and nilpotent groups
author_sort	Roman′kov, V. A.
journal	Siberian mathematical journal
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author-letter	Roman′kov, V. A.
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title_sort	commutator width of some relatively free lie algebras and nilpotent groups
title_auth	The commutator width of some relatively free lie algebras and nilpotent groups
abstract	Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank.
abstractGer	Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank.
abstract_unstemmed	Abstract We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ℚ-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank.
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container_issue	4
title_short	The commutator width of some relatively free lie algebras and nilpotent groups
url	https://dx.doi.org/10.1134/S0037446616040108
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doi_str	10.1134/S0037446616040108
up_date	2024-07-03T14:32:15.562Z
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The commutator width of some relatively free lie algebras and nilpotent groups

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