On one property of hypercyclic groups
We prove that the condition of periodicity of all normal Abelian subgroups of a group with increasing normal series with cyclic factors such that infinite factors are central is preserved on passing to subgroups of finite index. We present an example which demonstrates that the requirement that all...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5439 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511668927201280 |
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| author | Chechin, S. A. Чечин, С. А. Чечин, С. А. |
| author_facet | Chechin, S. A. Чечин, С. А. Чечин, С. А. |
| author_sort | Chechin, S. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T08:59:05Z |
| description | We prove that the condition of periodicity of all normal Abelian subgroups of a group with increasing normal series with cyclic factors such that infinite factors are central is preserved on passing to subgroups of finite index. We present an example which demonstrates that the requirement that all infinite cyclic factors must be central cannot be omitted. |
| first_indexed | 2026-03-24T03:16:33Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5439 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:16:33Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c6/7e5e56f217e4d6fdb0c70f981479a5c6.pdf |
| spelling | umjimathkievua-article-54392020-03-19T08:59:05Z On one property of hypercyclic groups Об одном свойстве гиперциклических групп Chechin, S. A. Чечин, С. А. Чечин, С. А. We prove that the condition of periodicity of all normal Abelian subgroups of a group with increasing normal series with cyclic factors such that infinite factors are central is preserved on passing to subgroups of finite index. We present an example which demonstrates that the requirement that all infinite cyclic factors must be central cannot be omitted. Доведено, що умова періодичності всіх нормальних абелевих підгруп групи, яка має зростаючий нормальний ряд з циклічними факторами, серед яких нескінченні фактори є центральними, зберігається при переході до підгруп скінченного індексу. Наведено приклад групи, який показує, що вимогою центральності всіх нескінченних циклічних факторів не можна нехтувати. Institute of Mathematics, NAS of Ukraine 1995-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5439 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 3 (1995); 436-438 Український математичний журнал; Том 47 № 3 (1995); 436-438 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5439/7567 https://umj.imath.kiev.ua/index.php/umj/article/view/5439/7568 Copyright (c) 1995 Chechin S. A. |
| spellingShingle | Chechin, S. A. Чечин, С. А. Чечин, С. А. On one property of hypercyclic groups |
| title | On one property of hypercyclic groups |
| title_alt | Об одном свойстве гиперциклических групп |
| title_full | On one property of hypercyclic groups |
| title_fullStr | On one property of hypercyclic groups |
| title_full_unstemmed | On one property of hypercyclic groups |
| title_short | On one property of hypercyclic groups |
| title_sort | on one property of hypercyclic groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5439 |
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