Whitehead algorithm for automorphisms of generalized Baumslag-Solitar groups

Abstract

In analogy with the free factors of a free group we define special factors of Generalized Baumslag-Solitar (GBS) groups as non-cyclic subgroups which appear in splittings over infinite cyclic groups. We give an algorithm which, given a GBS group $G$ and an element $g\in G$, decides whether there exists a special factor $H<G$ such that $g\in H$. This algorithm is analogous to an algorithm by Whitehead for free groups. Furthermore we prove that given $g\in G$ there exists a unique minimal special factor containing $g$ and give an algorithm which finds it.

42 pages, 15 figures

References in corpus (1)

• Algebraic laminations for free products and arational trees