This article is cited in 7 papers

On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups

E. V. Sokolov

Ivanovo State University

Abstract: Let $\mathcal{C}$ be an arbitrary class of groups which has the root property, consists of finite groups only, and contains at least one nonidentity group. It is proved that every extension of a free group by a $\mathcal{C}$-group is conjugacy $\mathcal{C}$-separable. It is also proved that, if $G$ is a free product of two conjugacy $\mathcal{C}$-separable groups with finite amalgamated subgroup or an HNN-extension of a conjugacy $\mathcal{C}$-separable group with finite associated subgroups, then the group $G$ is residually $\mathcal{C}$ if and only if it is conjugacy $\mathcal{C}$-separable.

Keywords: class of groups which has the root property, HNN-extension, free product with finite amalgamated subgroup, residually $\mathcal{C}$ group, conjugacy $\mathcal{C}$-separable group.

UDC: 512.543

Received: 22.09.2013

DOI: 10.4213/mzm10396

 English version: Mathematical Notes, 2015, 97:5, 779–790

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