On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank
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...
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Yaroslavl State University
2013-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/224 |
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| author | A. V. Rozov |
| author_facet | A. V. Rozov |
| author_sort | A. V. Rozov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ffafa3e92ddc488bad63c40916657607 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2013-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-ffafa3e92ddc488bad63c409166576072025-08-20T04:00:26ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-02-0120112413210.18255/1818-1015-2013-1-124-132217On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite RankA. V. Rozov0Ivanovo State UniversityLet 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.https://www.mais-journal.ru/jour/article/view/224soluble group of finite rankgeneralized free productresidually finite groupfinitely separable subgroup |
| spellingShingle | A. V. Rozov On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank Моделирование и анализ информационных систем soluble group of finite rank generalized free product residually finite group finitely separable subgroup |
| 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 | soluble group of finite rank generalized free product residually finite group finitely separable subgroup |
| url | https://www.mais-journal.ru/jour/article/view/224 |
| work_keys_str_mv | AT avrozov ontheresidualfinitenessofsomegeneralizedproductsofsolublegroupsoffiniterank |