Powers with minimal commutator length in free products of groups

Vadim Bereznyuk

Published 2022-06-12Version 1

Given a free product of groups $G = {\large *}_{j \in J} A_j$ and a natural number $n$, what is the minimal possible commutator length of an element $g^n \in G$ not conjugate to elements of the free factors? We give an exhaustive answer to this question.