Geometry & Topology 11 (2007) 473–515

DOI: 10.2140/gt.2007.11.473

arXiv: math.GR/0511083

Abstract

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 ≤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×Z), then Out(G) is commensurable with a semi-direct product Z^k⋊Out(H) with H virtually free.

Keywords

Baumslag–Solitar, automorphisms, graphs of groups

Mathematical Subject Classification

Primary: 20F65

Secondary: 20E08, 20F28

References

Forward citations

Publication

Received: 2005
Accepted: 2006
Published: 16 March 2007
Proposed: Martin Bridson
Seconded: Walter Neumann, Wolfgang Lueck

Authors