On the Separability of Abelian Subgroups of the Fundamental Groups of Graphs of Groups. II

Consider the fundamental group (Formula presented.) of an arbitrary graph of groupsand some root class (Formula presented.) of groups,i.e., a class containing a nontrivial groupand closed under subgroups,extensions,and unrestricted direct products of the form (Formula presented.),where (Formula presented.) and (Formula presented.) is an isomorphic copy of (Formula presented.) for each (Formula presented.).We provide some criterion for the separability by (Formula presented.) of a finitely generated abelian subgroup of (Formula presented.) valid whenthe group satisfies an analog of the Baumslag filtration condition.This enables us to describethe (Formula presented.) -separable finitely generated abelian subgroupsfor the fundamental groups of some graphs of groupswith central edge subgroups. © Pleiades Publishing, Ltd. 2024. Russian Text The Author(s), 2024, published in Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 1, pp. 207–228.