On the cyclic subgroup separability of the free product of two groups with commuting subgroups

E. V. Sokolov

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arXiv · 1308.1976

On the cyclic subgroup separability of the free product of two groups with commuting subgroups

E. V. Sokolov

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Abstract

Let G be the free product of groups A and B with commuting subgroups H \leqslant A and K \leqslant B, and let C be the class of all finite groups or the class of all finite p-groups. We derive the description of all C-separable cyclic subgroups of G provided this group is residually a C-group. We prove, in particular, that if A, B are finitely generated nilpotent groups and H, K are p'-isolated in the free factors, then all p'-isolated cyclic subgroups of G are separable in the class of all finite p-groups. The same statement is true provided A, B are free and H, K are p'-isolated and cyclic.

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BibTeX RIS

E. V. Sokolov. 2013-08-08. On the cyclic subgroup separability of the free product of two groups with commuting subgroups. https://arxiv.org/abs/1308.1976

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