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/...
Збережено в:
| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152792 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152792 |
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dspace |
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irk-123456789-1527922019-06-13T01:25:03Z On subgroups of finite exponent in groups Artemovych, O.D. 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. 2015 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152792 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Artemovych, O.D. |
| spellingShingle |
Artemovych, O.D. On subgroups of finite exponent in groups Algebra and Discrete Mathematics |
| author_facet |
Artemovych, O.D. |
| author_sort |
Artemovych, O.D. |
| title |
On subgroups of finite exponent in groups |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT artemovychod onsubgroupsoffiniteexponentingroups |
| first_indexed |
2023-05-20T17:38:15Z |
| last_indexed |
2023-05-20T17:38:15Z |
| _version_ |
1796153748427374592 |