This article is cited in 1 paper

Torsion in the outer automorphism groups of generalized Baumslag–Solitar groups

F. A. Dudkin^a, N. Yang<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Jiangnan University

Abstract: A generalized Baumslag–Solitar group ($GBS$-group) is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. It is known that the outer automorphism groups of some $GBS$ groups contain some $p$-torsion of unbounded order. We prove that in this case the prime $p$ divides the integral modulus of $G$. This result answers Levitt's question.

Keywords: generalized Baumslag–Solitar group, outer automorphism group, automorphism, automorphism of finite order.

UDC: 512.54

MSC: 35R30

Received: 17.03.2022
Revised: 18.04.2022
Accepted: 15.06.2022

DOI: 10.33048/smzh.2023.64.108

 English version: Siberian Mathematical Journal, 2023, 64:1, 67–75