On the Automorphism Group of Generalized Baumslag-solitar Groups
نویسنده
چکیده
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 Fn × Z), then Out(G) is commensurable with a semi-direct product Z ⋊Out(H) with H virtually free.
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