On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank
<p>Let G be a free product of residually finite virtually soluble groups A and B of finite rank with an amalgamated subgroup H, H 6= A and H 6= B. And let H contains a subgroup W of finite index which is normal in both A and B. We prove that the group G is residually finite if and only if the...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-01-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | http://mais-journal.ru/jour/article/view/224 |
| _version_ | 1797965932595773440 |
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| author | A. V. Rozov |
| author_facet | A. V. Rozov |
| author_sort | A. V. Rozov |
| collection | DOAJ |
| description | <p>Let G be a free product of residually finite virtually soluble groups A and B of finite rank with an amalgamated subgroup H, H 6= A and H 6= B. And let H contains a subgroup W of finite index which is normal in both A and B. We prove that the group G is residually finite if and only if the subgroup H is finitely separable in A and B. Also we prove that if all subgroups of A and B are finitely separable in A and B, respectively, all finitely generated subgroups of G are finitely separable in G.</p> |
| first_indexed | 2024-04-11T02:07:48Z |
| format | Article |
| id | doaj.art-d842f10624294f0b8cb25fadf02602a9 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-11T02:07:48Z |
| publishDate | 2013-01-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-d842f10624294f0b8cb25fadf02602a92023-01-03T02:50:20ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-01-01201124132217On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite RankA. V. Rozov0Ивановский государственный университет<p>Let G be a free product of residually finite virtually soluble groups A and B of finite rank with an amalgamated subgroup H, H 6= A and H 6= B. And let H contains a subgroup W of finite index which is normal in both A and B. We prove that the group G is residually finite if and only if the subgroup H is finitely separable in A and B. Also we prove that if all subgroups of A and B are finitely separable in A and B, respectively, all finitely generated subgroups of G are finitely separable in G.</p>http://mais-journal.ru/jour/article/view/224Разрешимая группа конечного рангаобобщенное свободное произведение группфинитно аппроксимируемая группафинитно отделимая подгруппа |
| spellingShingle | A. V. Rozov On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank Моделирование и анализ информационных систем Разрешимая группа конечного ранга обобщенное свободное произведение групп финитно аппроксимируемая группа финитно отделимая подгруппа |
| title | On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank |
| title_full | On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank |
| title_fullStr | On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank |
| title_full_unstemmed | On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank |
| title_short | On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank |
| title_sort | on the residual finiteness of some generalized products of soluble groups of finite rank |
| topic | Разрешимая группа конечного ранга обобщенное свободное произведение групп финитно аппроксимируемая группа финитно отделимая подгруппа |
| url | http://mais-journal.ru/jour/article/view/224 |
| work_keys_str_mv | AT avrozov ontheresidualfinitenessofsomegeneralizedproductsofsolublegroupsoffiniterank |