|
Lobachevskii Journal of Mathematics, 2002, Volume 11, Pages 27–38
(Mi ljm118)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
On the cyclic subgroup separability of free products of two groups with amalgamated subgroup
E. V. Sokolov Ivanovo State University
Abstract:
Let $G$ be a free product of two groups with amalgamated subgroup, $\pi$ be either the set of all prime numbers or the one-element set $\{p\}$ for some prime number $p$. Denote by $\sum$ the family of all cyclic subgroups of group $G$, which are separable in the class of all finite $\pi$-groups. Obviously, cyclic subgroups of the free factors, which aren't separable in these factors by the family of all normal subgroups of finite $\pi$-index of group $G$, the
subgroups conjugated with them and all subgroups, which aren't $\pi'$-isolated,
don't belong to $\sum$. Some sufficient conditions are obtained for $\sum$ to coincide
with the family of all other $\pi'$-isolated cyclic subgroups of group $G$.
It is proved, in particular, that the residual $\pi'$-finiteness of a free product with cyclic amalgamation implies the $p$-separability of all $p'$-isolated cyclic
subgroups if the free factors are free or finitely generated residually $p$-finite
nilpotent groups.
Keywords:
Generalized free products, cyclic subgroup separability.
Citation:
E. V. Sokolov, “On the cyclic subgroup separability of free products of two groups with amalgamated subgroup”, Lobachevskii J. Math., 11 (2002), 27–38
Linking options:
https://www.mathnet.ru/eng/ljm118 https://www.mathnet.ru/eng/ljm/v11/p27
|
Statistics & downloads: |
Abstract page: | 195 | Full-text PDF : | 94 | References: | 66 |
|