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- W1617606536 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 $Sigma$ 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 $pi^{prime}$-isolated, don't belong to $Sigma$. Some sufficient conditions are obtained for $Sigma$ to coincide with the family of all other $pi^{prime}$-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." @default.
- W1617606536 created "2016-06-24" @default.
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- W1617606536 date "2007-08-21" @default.
- W1617606536 modified "2023-09-27" @default.
- W1617606536 title "On the cyclic subgroup separability of free products of two groups with amalgamated subgroup" @default.
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