On the automorphism group of generalized Baumslag-Solitar groups

Details On the automorphism group of generalized Baumslag-Solitar groups On the automorphism group of generalized Baumslag-Solitar groups

2005-11-03

arxiv.org/abs/math/0511083v1

Geometry & Topology 11 (2007), 473-515

Mathematics

Group Theory

Scientific paper

A generalized Baumslag-Solitar group (GBS group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains non-abelian free groups or is virtually nilpotent of class at most 2. It has torsion only at finitely many primes. One may decide algorithmically whether Out(G) is virtually nilpotent or not. If it is, one may decide whether it is virtually abelian, or finitely generated. The isomorphism problem is solvable among GBS groups with Out(G) virtually nilpotent. If $G$ is unimodular (virtually $F_n \times Z$), then Out(G) is commensurable with a semi-direct product $Z^k \rtimes Out(H)$ with $H$ virtually free.

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