On the Subgroup Separability of Generalized Free Products of Nilpotent Groups

On the Cyclic Subgroup Separability of Free Products of Two Groups with Amalgamated Subgroup

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 subgro...

Subgroup Separability in Residually Free Groups

We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type FP∞ are virtual retracts. We describe a uniform solution to the membership problem for finitely presentable subgroups of residually free groups.

On the Residual Solvability of Generalized Free Products of Finitely Generated Nilpotent Groups

In this paper we study the residual solvability of the generalized free product of finitely generated nilpotent groups. We show that these kinds of structures are often residually solvable.

On Subgroup Separability in Hyperbolic Coxeter Groups

On Subgroup Separability in Hyperbolic Coxeter Groups

We prove that certain hyperbolic Coxeter groups are separable on their geometrically ¢nite subgroups. Mathematics Subject Classi¢cation (2000). 20H10. Key words. hyperbolic Coxeter group, subgroup separability. 1. Introduction Recall that a subgroupH of a group G is separable in G if, given any g 2 G nH, there exists a subgroup K < G of ¢nite index with H < K and g = 2K . G is called subgroup s...