Consider the fundamental group \( {\mathfrak{G}} \) of an arbitrary graph of groups and some root class \( {\mathcal{C}} \) of groups, i.e., a class containing a nontrivial group and closed under subgroups, extensions, and unrestricted direct products of the form \( \prod_{y\in Y}X_{y} \), where \( X,Y\in{\mathcal{C}} \) and \( X_{y} \) is an isomorphic copy of \( X \) for each \( y\in Y \). We provide some criterion for the separability by \( {\mathcal{C}} \) of a finitely generated abelian subgroup of \( {\mathfrak{G}} \) valid when the group satisfies an analog of the Baumslag filtration condition. This enables us to describe the \( {\mathcal{C}} \)-separable finitely generated abelian subgroups for the fundamental groups of some graphs of groups with central edge subgroups.

考虑任意群图的 基本群 \( {\mathfrak{G}} \)和群的某个根类\( {\mathcal{C}} \) ，即包含非平凡群并在下封闭的类子群、扩展和无限制直积，其形式为 \( \prod_{y\in Y}X_{y} \)，其中 \( X,Y\in{\mathcal{C}} \) 和 \( X_{ y} \)是 每个 \( y\in Y \)的\( X \) 的同构副本 。我们为 \( {\mathfrak{G}} \) 的有限生成阿贝尔子群的 \( {\mathcal{C}} \)的可分离性提供了一些标准 ，当该群满足鲍姆斯拉格过滤条件的模拟时，该标准有效。这使我们能够为某些具有中心边子群的群的图的基本群描述\( {\mathcal{C}} \)可分离的有限生成的阿贝尔子群。