Small, nm-stable compact G-groups

Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable com...
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Autor*in:	Krupiński, Krzysztof [verfasserIn] Wagner, Frank

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2012

Schlagwörter:	Closed Subgroup Inverse Limit Polish Structure Open Subgroup Inverse System

Anmerkung:	© Hebrew University Magnes Press 2012

Übergeordnetes Werk:	Enthalten in: Israel journal of mathematics - Berlin : Springer, 1963, 194(2012), 2 vom: 13. Juli, Seite 907-933
Übergeordnetes Werk:	volume:194 ; year:2012 ; number:2 ; day:13 ; month:07 ; pages:907-933

Links:	Volltext

DOI / URN:	10.1007/s11856-012-0103-3

Katalog-ID:	SPR022824685

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520			\|a Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank.
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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_213
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912			\|a GBV_ILN_230
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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
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912			\|a GBV_ILN_2003
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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
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912			\|a GBV_ILN_2061
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912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
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Indexfelder

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publishDate	2012
allfields	10.1007/s11856-012-0103-3 doi (DE-627)SPR022824685 (SPR)s11856-012-0103-3-e DE-627 ger DE-627 rakwb eng Krupiński, Krzysztof verfasserin aut Small, nm-stable compact G-groups 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2012 Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. Closed Subgroup (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Polish Structure (dpeaa)DE-He213 Open Subgroup (dpeaa)DE-He213 Inverse System (dpeaa)DE-He213 Wagner, Frank aut Enthalten in Israel journal of mathematics Berlin : Springer, 1963 194(2012), 2 vom: 13. Juli, Seite 907-933 (DE-627)32654528X (DE-600)2042388-3 1565-8511 nnns volume:194 year:2012 number:2 day:13 month:07 pages:907-933 https://dx.doi.org/10.1007/s11856-012-0103-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 AR 194 2012 2 13 07 907-933
spelling	10.1007/s11856-012-0103-3 doi (DE-627)SPR022824685 (SPR)s11856-012-0103-3-e DE-627 ger DE-627 rakwb eng Krupiński, Krzysztof verfasserin aut Small, nm-stable compact G-groups 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2012 Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. Closed Subgroup (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Polish Structure (dpeaa)DE-He213 Open Subgroup (dpeaa)DE-He213 Inverse System (dpeaa)DE-He213 Wagner, Frank aut Enthalten in Israel journal of mathematics Berlin : Springer, 1963 194(2012), 2 vom: 13. Juli, Seite 907-933 (DE-627)32654528X (DE-600)2042388-3 1565-8511 nnns volume:194 year:2012 number:2 day:13 month:07 pages:907-933 https://dx.doi.org/10.1007/s11856-012-0103-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 AR 194 2012 2 13 07 907-933
allfields_unstemmed	10.1007/s11856-012-0103-3 doi (DE-627)SPR022824685 (SPR)s11856-012-0103-3-e DE-627 ger DE-627 rakwb eng Krupiński, Krzysztof verfasserin aut Small, nm-stable compact G-groups 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2012 Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. Closed Subgroup (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Polish Structure (dpeaa)DE-He213 Open Subgroup (dpeaa)DE-He213 Inverse System (dpeaa)DE-He213 Wagner, Frank aut Enthalten in Israel journal of mathematics Berlin : Springer, 1963 194(2012), 2 vom: 13. Juli, Seite 907-933 (DE-627)32654528X (DE-600)2042388-3 1565-8511 nnns volume:194 year:2012 number:2 day:13 month:07 pages:907-933 https://dx.doi.org/10.1007/s11856-012-0103-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 AR 194 2012 2 13 07 907-933
allfieldsGer	10.1007/s11856-012-0103-3 doi (DE-627)SPR022824685 (SPR)s11856-012-0103-3-e DE-627 ger DE-627 rakwb eng Krupiński, Krzysztof verfasserin aut Small, nm-stable compact G-groups 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2012 Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. Closed Subgroup (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Polish Structure (dpeaa)DE-He213 Open Subgroup (dpeaa)DE-He213 Inverse System (dpeaa)DE-He213 Wagner, Frank aut Enthalten in Israel journal of mathematics Berlin : Springer, 1963 194(2012), 2 vom: 13. Juli, Seite 907-933 (DE-627)32654528X (DE-600)2042388-3 1565-8511 nnns volume:194 year:2012 number:2 day:13 month:07 pages:907-933 https://dx.doi.org/10.1007/s11856-012-0103-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 AR 194 2012 2 13 07 907-933
allfieldsSound	10.1007/s11856-012-0103-3 doi (DE-627)SPR022824685 (SPR)s11856-012-0103-3-e DE-627 ger DE-627 rakwb eng Krupiński, Krzysztof verfasserin aut Small, nm-stable compact G-groups 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Hebrew University Magnes Press 2012 Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. Closed Subgroup (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Polish Structure (dpeaa)DE-He213 Open Subgroup (dpeaa)DE-He213 Inverse System (dpeaa)DE-He213 Wagner, Frank aut Enthalten in Israel journal of mathematics Berlin : Springer, 1963 194(2012), 2 vom: 13. Juli, Seite 907-933 (DE-627)32654528X (DE-600)2042388-3 1565-8511 nnns volume:194 year:2012 number:2 day:13 month:07 pages:907-933 https://dx.doi.org/10.1007/s11856-012-0103-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_65 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_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_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_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 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 AR 194 2012 2 13 07 907-933
language	English
source	Enthalten in Israel journal of mathematics 194(2012), 2 vom: 13. Juli, Seite 907-933 volume:194 year:2012 number:2 day:13 month:07 pages:907-933
sourceStr	Enthalten in Israel journal of mathematics 194(2012), 2 vom: 13. Juli, Seite 907-933 volume:194 year:2012 number:2 day:13 month:07 pages:907-933
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Closed Subgroup Inverse Limit Polish Structure Open Subgroup Inverse System
isfreeaccess_bool	false
container_title	Israel journal of mathematics
authorswithroles_txt_mv	Krupiński, Krzysztof @@aut@@ Wagner, Frank @@aut@@
publishDateDaySort_date	2012-07-13T00:00:00Z
hierarchy_top_id	32654528X
id	SPR022824685
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author	Krupiński, Krzysztof
spellingShingle	Krupiński, Krzysztof misc Closed Subgroup misc Inverse Limit misc Polish Structure misc Open Subgroup misc Inverse System Small, nm-stable compact G-groups
authorStr	Krupiński, Krzysztof
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topic_title	Small, nm-stable compact G-groups Closed Subgroup (dpeaa)DE-He213 Inverse Limit (dpeaa)DE-He213 Polish Structure (dpeaa)DE-He213 Open Subgroup (dpeaa)DE-He213 Inverse System (dpeaa)DE-He213
topic	misc Closed Subgroup misc Inverse Limit misc Polish Structure misc Open Subgroup misc Inverse System
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title	Small, nm-stable compact G-groups
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title_full	Small, nm-stable compact G-groups
author_sort	Krupiński, Krzysztof
journal	Israel journal of mathematics
journalStr	Israel journal of mathematics
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author_browse	Krupiński, Krzysztof Wagner, Frank
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author-letter	Krupiński, Krzysztof
doi_str_mv	10.1007/s11856-012-0103-3
title_sort	small, nm-stable compact g-groups
title_auth	Small, nm-stable compact G-groups
abstract	Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. © Hebrew University Magnes Press 2012
abstractGer	Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. © Hebrew University Magnes Press 2012
abstract_unstemmed	Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. We provide counter-examples to the NM-gap conjecture, that is we give examples of small, nm-stable compact G-groups of infinite ordinal NM-rank. © Hebrew University Magnes Press 2012
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title_short	Small, nm-stable compact G-groups
url	https://dx.doi.org/10.1007/s11856-012-0103-3
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doi_str	10.1007/s11856-012-0103-3
up_date	2024-07-03T15:05:55.314Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR022824685</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230330070832.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201006s2012 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11856-012-0103-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR022824685</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11856-012-0103-3-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krupiński, Krzysztof</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Small, nm-stable compact G-groups</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2012</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Hebrew University Magnes Press 2012</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We prove that if (H, G) is a small, nm-stable compact G-group, then H is nilpotent-by-finite, and if additionally NM(H) < ω or NM(H) = ωα for some ordinal α, then H is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, nm-stable compact G-group is abelian-by-finite. 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