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

E. V. Sokolov

Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 767-780

Résumé

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.

Détail

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.