Whitehead algorithm for generalized Baumslag-Solitar groups
Chloé Papin · HAL (Le Centre pour la Communication Scientifique Directe) · 2022
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 ∈ G, decides whether there exists a special factor H < G such that g ∈ H. This algorithm is analogous to an algorithm by Whitehead for free groups. Furthermore we prove that given g ∈ G there exists a unique minimal special factor containing g and give an algorithm which finds it.