Isomorphism criterion for GBS(n,1) groups with non-trivial center
0000-0002-4775-7962 The material was received by the Editorial Board: 23.01.2026
A finitely generated group $G_n$ that acts on a tree $T$ such that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free Abelian groups of rank $n$ will be called a {\it generalized Baumslag--Solitar group of type (n,1)} ($GBS(n,1)$ group). Recently, the author found necessary conditions for the isomorphism of such groups with a non-trivial center. In this paper, we extend these conditions to a criterion. The proposed conditions can be verified algorithmically.
УДК 512.54
Keywords: generalized Baumslag--Solitar group, isomorphism problem, group with non-trivial center.
References: Dudkin F.A. Isomorphism criterion for GBS(n,1) groups with non-trivial center. Mat. Trudy. 2026, 29, № 2. P. 22–32. DOI: 10.25205/1560-750X-2026-29-2-22-32