Central Extensions of %${n}%$-Torsion Groups
Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators....
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Atabekyan, V. S. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Anmerkung: |
© Allerton Press, Inc. 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of contemporary mathematical analysis - New York, NY : Allerton, 2007, 57(2022), 1 vom: Feb., Seite 26-34 |
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| Übergeordnetes Werk: |
volume:57 ; year:2022 ; number:1 ; month:02 ; pages:26-34 |
| Links: |
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| DOI / URN: |
10.3103/S1068362322010034 |
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| Katalog-ID: |
SPR050563416 |
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| 100 | 1 | |a Atabekyan, V. S. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Central Extensions of %${n}%$-Torsion Groups |
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| 520 | |a Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. | ||
| 700 | 1 | |a Gevorkyan, G. G. |4 aut | |
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10.3103/S1068362322010034 doi (DE-627)SPR050563416 (SPR)S1068362322010034-e DE-627 ger DE-627 rakwb eng Atabekyan, V. S. verfasserin aut Central Extensions of %${n}%$-Torsion Groups 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Allerton Press, Inc. 2022 Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. Gevorkyan, G. G. aut Enthalten in Journal of contemporary mathematical analysis New York, NY : Allerton, 2007 57(2022), 1 vom: Feb., Seite 26-34 (DE-627)535186851 (DE-600)2375727-9 1934-9416 nnns volume:57 year:2022 number:1 month:02 pages:26-34 https://dx.doi.org/10.3103/S1068362322010034 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 57 2022 1 02 26-34 |
| spelling |
10.3103/S1068362322010034 doi (DE-627)SPR050563416 (SPR)S1068362322010034-e DE-627 ger DE-627 rakwb eng Atabekyan, V. S. verfasserin aut Central Extensions of %${n}%$-Torsion Groups 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Allerton Press, Inc. 2022 Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. Gevorkyan, G. G. aut Enthalten in Journal of contemporary mathematical analysis New York, NY : Allerton, 2007 57(2022), 1 vom: Feb., Seite 26-34 (DE-627)535186851 (DE-600)2375727-9 1934-9416 nnns volume:57 year:2022 number:1 month:02 pages:26-34 https://dx.doi.org/10.3103/S1068362322010034 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 57 2022 1 02 26-34 |
| allfields_unstemmed |
10.3103/S1068362322010034 doi (DE-627)SPR050563416 (SPR)S1068362322010034-e DE-627 ger DE-627 rakwb eng Atabekyan, V. S. verfasserin aut Central Extensions of %${n}%$-Torsion Groups 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Allerton Press, Inc. 2022 Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. Gevorkyan, G. G. aut Enthalten in Journal of contemporary mathematical analysis New York, NY : Allerton, 2007 57(2022), 1 vom: Feb., Seite 26-34 (DE-627)535186851 (DE-600)2375727-9 1934-9416 nnns volume:57 year:2022 number:1 month:02 pages:26-34 https://dx.doi.org/10.3103/S1068362322010034 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 57 2022 1 02 26-34 |
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10.3103/S1068362322010034 doi (DE-627)SPR050563416 (SPR)S1068362322010034-e DE-627 ger DE-627 rakwb eng Atabekyan, V. S. verfasserin aut Central Extensions of %${n}%$-Torsion Groups 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Allerton Press, Inc. 2022 Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. Gevorkyan, G. G. aut Enthalten in Journal of contemporary mathematical analysis New York, NY : Allerton, 2007 57(2022), 1 vom: Feb., Seite 26-34 (DE-627)535186851 (DE-600)2375727-9 1934-9416 nnns volume:57 year:2022 number:1 month:02 pages:26-34 https://dx.doi.org/10.3103/S1068362322010034 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 57 2022 1 02 26-34 |
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10.3103/S1068362322010034 doi (DE-627)SPR050563416 (SPR)S1068362322010034-e DE-627 ger DE-627 rakwb eng Atabekyan, V. S. verfasserin aut Central Extensions of %${n}%$-Torsion Groups 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Allerton Press, Inc. 2022 Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. Gevorkyan, G. G. aut Enthalten in Journal of contemporary mathematical analysis New York, NY : Allerton, 2007 57(2022), 1 vom: Feb., Seite 26-34 (DE-627)535186851 (DE-600)2375727-9 1934-9416 nnns volume:57 year:2022 number:1 month:02 pages:26-34 https://dx.doi.org/10.3103/S1068362322010034 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 57 2022 1 02 26-34 |
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Central Extensions of %${n}%$-Torsion Groups |
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Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. © Allerton Press, Inc. 2022 |
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Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. © Allerton Press, Inc. 2022 |
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Abstract For %$n%$-torsion groups of odd period %$n\geq 1003%$, we construct a certain modification of the method invented by S.I. Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$. © Allerton Press, Inc. 2022 |
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Adian to positively solve the well-known problem of the existence of noncommutative analogs of the additive group of rational numbers with a finite number of generators. Using this modification, we prove that any %$m%$-generated Abelian group %$D%$ can be embedded as a center into some group %$A%$ so that the quotient group %$A/D%$ is isomorphic to a given %$n%$-torsion group with at least %$m%$ independent defining relations. As an application, it is proved that every subgroup of any %$n%$-torsion group is cyclic, which generalizes a similar result proved earlier by S.I. Adian for free Burnside groups of odd period %$n\geq 665%$. Note that the set of nonisomorphic %$s%$-generated %$n%$-torsion groups has a cardinality of the continuum for fixed %$s>1%$ and any odd %$n\geq 1003%$.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gevorkyan, G. 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