On the cyclic subgroup separability of free products of two groups with amalgamated subgroup
| dc.creator | Sokolov, E. V. | |
| dc.date | 2007-08-21 | |
| dc.date.accessioned | 2026-07-07T08:24:44Z | |
| dc.date.available | 2026-07-07T08:24:44Z | |
| dc.description | Let $G$ be a free product of two groups with amalgamated subgroup, $π$ be either the set of all prime numbers or the one-element set \{$p$\} for some prime number $p$. Denote by $Σ$ the family of all cyclic subgroups of group $G$, which are separable in the class of all finite $π$-groups. Obviously, cyclic subgroups of the free factors, which aren't separable in these factors by the family of all normal subgroups of finite $π$-index of group $G$, the subgroups conjugated with them and all subgroups, which aren't $π^{\prime}$-isolated, don't belong to $Σ$. Some sufficient conditions are obtained for $Σ$ to coincide with the family of all other $π^{\prime}$-isolated cyclic subgroups of group $G$. It is proved, in particular, that the residual $p$-finiteness of a free product with cyclic amalgamation implies the $p$-separability of all $p^{\prime}$-isolated cyclic subgroups if the free factors are free or finitely generated residually $p$-finite nilpotent groups. | |
| dc.description | 10 pages; for other papers of this author, see http://icu.ivanovo.ac.ru/tg-seminar | |
| dc.identifier | https://arxiv.org/abs/0708.2819 | |
| dc.identifier | http://arxiv.org/abs/0708.2819 | |
| dc.identifier | Lobachevskii Journal of Mathematics. 11 (2002). 27-38 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136440 | |
| dc.subject | Group Theory | |
| dc.subject | 20E06, 20E26 (Primary) | |
| dc.title | On the cyclic subgroup separability of free products of two groups with amalgamated subgroup | |
| dc.type | text |