On the Separability of Abelian Subgroups of the Generalized Free Product of Two Groups with Normal Amalgamated Subgroup

Consider some class $ C $ of groups that is closed under subgroups, quotients, and unrestricted wreath products, and let $ G $ be the generalized free product of groups $ A $ and $ B $ with an amalgamated subgroup $ H $ , which is a normal and proper subgroup of the free factors. Suppose that the subgroup of the automorphism group of $ H $ consisting of the restrictions to $ H $ of all inner automorphisms of $ G $ is finite, or abelian, or generated by the restrictions of inner automorphisms of one of the free factors. In this article we describe the $ C $ -separable finitely generated abelian subgroups of $ G $ on assuming that the latter is a residually $ C $ -group. A criterion for the $ C $ -residuality of $ G $ is available.