Abstract
Let 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 C-group is conjugacy C-separable. It is also proved that, if G is a free product of two conjugacy C-separable groups with finite amalgamated subgroup or an HNN-extension of a conjugacy C-separable group with finite associated subgroups, then the group G is residually C if and only if it is conjugacy C-separable.
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Original Russian Text © E. V. Sokolov, 2015, published in Matematicheskie Zametki, 2015, Vol. 97, No. 5, pp. 767–780.
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Sokolov, E.V. On the conjugacy separability of some free constructions of groups by root classes of finite groups. Math Notes 97, 779–790 (2015). https://doi.org/10.1134/S0001434615050132
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DOI: https://doi.org/10.1134/S0001434615050132