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-...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2015 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152792 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862660020504625152 |
|---|---|
| author | Artemovych, O.D. |
| author_facet | Artemovych, O.D. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-12-02T10:29:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152792 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T10:29:30Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On subgroups of finite exponent in groups Artemovych, O.D. |
| title | 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_short | On subgroups of finite exponent in groups |
| title_sort | on subgroups of finite exponent in groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152792 |
| work_keys_str_mv | AT artemovychod onsubgroupsoffiniteexponentingroups |