On subgroups of finite exponent in groups
We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group G of infinite exponent with all proper subgroups of finite exponent has the following properties: (1) G is an indecomposable p-group, (2) if the derived subgroup G′ is non-perfect, then G/...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152792 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On subgroups of finite exponent in groups / O.D. Artemovych // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 1-7. — Бібліогр.: 13 назв. — англ. |
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Artemovych, O.D. 2019-06-12T20:59:40Z 2019-06-12T20:59:40Z 2015 On subgroups of finite exponent in groups / O.D. Artemovych // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 1-7. — Бібліогр.: 13 назв. — англ. 1726-3255 2010 MSC:20F50, 20F26, 20E26. https://nasplib.isofts.kiev.ua/handle/123456789/152792 We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group G of infinite exponent with all proper subgroups of finite exponent has the following properties: (1) G is an indecomposable p-group, (2) if the derived subgroup G′ is non-perfect, then G/G′′ is a group of Heineken-Mohamed type. We also prove that a non-perfect indecomposable group G with the non-perfect locally nilpotent derived subgroup G′ is a locally finite p-group. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On subgroups of finite exponent in groups Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On subgroups of finite exponent in groups |
| spellingShingle |
On subgroups of finite exponent in groups Artemovych, O.D. |
| title_short |
On subgroups of finite exponent in groups |
| title_full |
On subgroups of finite exponent in groups |
| title_fullStr |
On subgroups of finite exponent in groups |
| title_full_unstemmed |
On subgroups of finite exponent in groups |
| title_sort |
on subgroups of finite exponent in groups |
| author |
Artemovych, O.D. |
| author_facet |
Artemovych, O.D. |
| publishDate |
2015 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group G of infinite exponent with all proper subgroups of finite exponent has the following properties:
(1) G is an indecomposable p-group,
(2) if the derived subgroup G′ is non-perfect, then G/G′′ is a group of Heineken-Mohamed type.
We also prove that a non-perfect indecomposable group G with the non-perfect locally nilpotent derived subgroup G′ is a locally finite p-group.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/152792 |
| citation_txt |
On subgroups of finite exponent in groups / O.D. Artemovych // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 1-7. — Бібліогр.: 13 назв. — англ. |
| work_keys_str_mv |
AT artemovychod onsubgroupsoffiniteexponentingroups |
| first_indexed |
2025-12-02T10:29:30Z |
| last_indexed |
2025-12-02T10:29:30Z |
| _version_ |
1850862274681503744 |