Powers with minimal commutator length in free products of groups

Vadim Bereznyuk

doi:10.1016/j.jalgebra.2023.04.008

paper

Powers with minimal commutator length in free products of groups

arXiv:2206.05795 · doi:10.1016/j.jalgebra.2023.04.008

Abstract

Given a free product of groups $G = *_{j \in J} A_{j}$ 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.

14 pages, 11 figures. v2: better definition of path labels and other minor improvements

Powers with minimal commutator length in free products of groups

Abstract

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