On subgroup conjugacy separability in the class of virtually free groups

Abstract

A group G is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of G remain non-conjugate in some finite quotient of G. We prove that the free groups and the fundamental groups of finite trees of finite groups with some normalizer condition are SCS. We also introduce the subgroup into-conjugacy separability property and prove that the above groups have this property too.