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arXiv · 2008.02861

Commutator length of powers in free products of groups

Vadim Yu. Bereznyuk·Anton A. Klyachko
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Abstract

Given groups $A$ and $B$, what is the minimal commutator length of the 2020th (for instance) power of an element $g\in A*B$ 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 $A$ and $B$). Other similar problems are also considered.

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Vadim Yu. Bereznyuk, Anton A. Klyachko. 2020-08-06. Commutator length of powers in free products of groups. https://doi.org/10.1017/s0013091521000808

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