Geometry & Topology
- Geom. Topol.
- Volume 11, Number 1 (2007), 473-515.
On the automorphism group of generalized Baumslag–Solitar groups
A generalized Baumslag–Solitar group (GBS group) is a finitely generated group which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that 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 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 virtually nilpotent.
If is unimodular (virtually ), then is commensurable with a semi-direct product with virtually free.
Geom. Topol., Volume 11, Number 1 (2007), 473-515.
First available in Project Euclid: 20 December 2017
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Levitt, Gilbert. On the automorphism group of generalized Baumslag–Solitar groups. Geom. Topol. 11 (2007), no. 1, 473--515. doi:10.2140/gt.2007.11.473. https://projecteuclid.org/euclid.gt/1513799838