Powers with minimal commutator length in free products of groups

Vadim Bereznyuk

doi:10.1016/j.jalgebra.2023.04.008

Powers with minimal commutator length in free products of groups

Group Theory 2023-10-10 v2

Authors: Vadim Bereznyuk

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Abstract

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.

Keywords

free product of groups commutator length powers free factors group theory

Cite

@article{arxiv.2206.05795,
  title  = {Powers with minimal commutator length in free products of groups},
  author = {Vadim Bereznyuk},
  journal= {arXiv preprint arXiv:2206.05795},
  year   = {2023}
}

Comments

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

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