Commutator length of powers in free products of groups
Group Theory
2022-03-16 v4
Abstract
Given groups and , what is the minimal commutator length of the 2020th (for instance) power of an element not conjugate to elements of the free factors? The exhaustive answer to this question is still unknown, but we can give an almost answer: this minimum is one of two numbers (simply depending on and ). Other similar problems are also considered.
Keywords
Cite
@article{arxiv.2008.02861,
title = {Commutator length of powers in free products of groups},
author = {Vadim Yu. Bereznyuk and Anton A. Klyachko},
journal= {arXiv preprint arXiv:2008.02861},
year = {2022}
}
Comments
11 pages, 4 figures. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V2: misprints corrected. V3: several corrections in the proofs --- the results remain unchanged. V4: A misprint is corrected