On one question of B. Amberg
In the case where a group $G$ is the product $G = AB$ of Abelian subgroups $A$ and $B$, one of which has і finite 0-rank, it is proved that the Fitting subgroup $F$ and the Hirsch - Plotkin radical $R$ admit the lecompositions $F = (F \bigcap A)(F \bigcap B)$ and $R = (R \bigcap A)(R \bigcap B)$, r...
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| Date: | 1994 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5748 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511971307159552 |
|---|---|
| author | Sysak, Ya. P. Сысак, Я. П. Сысак, Я. П. |
| author_facet | Sysak, Ya. P. Сысак, Я. П. Сысак, Я. П. |
| author_sort | Sysak, Ya. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:16:47Z |
| description | In the case where a group $G$ is the product $G = AB$ of Abelian subgroups $A$ and $B$, one of which has і finite 0-rank,
it is proved that the Fitting subgroup $F$ and the Hirsch - Plotkin radical $R$ admit the lecompositions $F = (F \bigcap A)(F \bigcap B)$ and $R = (R \bigcap A)(R \bigcap B)$, respectively.
This gives the affinitive answer to B. Amberg's question. |
| first_indexed | 2026-03-24T03:21:22Z |
| format | Article |
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| id | umjimathkievua-article-5748 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:21:22Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/2f/514aee23c9750bf5677293e8b01af42f.pdf |
| spelling | umjimathkievua-article-57482020-03-19T09:16:47Z On one question of B. Amberg Об одном вопросе Б. Амберга Sysak, Ya. P. Сысак, Я. П. Сысак, Я. П. In the case where a group $G$ is the product $G = AB$ of Abelian subgroups $A$ and $B$, one of which has і finite 0-rank, it is proved that the Fitting subgroup $F$ and the Hirsch - Plotkin radical $R$ admit the lecompositions $F = (F \bigcap A)(F \bigcap B)$ and $R = (R \bigcap A)(R \bigcap B)$, respectively. This gives the affinitive answer to B. Amberg's question. Якщо група $G$ є добутком $G = AB$ абелевих підгруп $A$ і $B$, одна з яких має скінчений 0-ранг, доведено, що підгрупа Фіттінга $F$ і радикал Хірша - Плоткіна $R$ мають розклад $F = (F \bigcap A)(F \bigcap B)$. Це дає позитивну відповідь на одне запитання Б. Амберга. Institute of Mathematics, NAS of Ukraine 1994-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5748 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 4 (1994); 457–461 Український математичний журнал; Том 46 № 4 (1994); 457–461 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5748/8181 https://umj.imath.kiev.ua/index.php/umj/article/view/5748/8182 Copyright (c) 1994 Sysak Ya. P. |
| spellingShingle | Sysak, Ya. P. Сысак, Я. П. Сысак, Я. П. On one question of B. Amberg |
| title | On one question of B. Amberg |
| title_alt | Об одном вопросе Б. Амберга |
| title_full | On one question of B. Amberg |
| title_fullStr | On one question of B. Amberg |
| title_full_unstemmed | On one question of B. Amberg |
| title_short | On one question of B. Amberg |
| title_sort | on one question of b. amberg |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5748 |
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