Commutator length of powers in free products of groups

Abstract

Given groups $A$ and $B$, what is the minimal commutator length of the 2020th (for instance) power of an element $g\in A\ast B$ 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.

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

References in corpus (3)

• How to generalize known results on equations over groups
• Quasiperiodic and mixed commutator factorizations in free products of groups
• The SQ-universality of one-relator relative presentations

Cited by in corpus (1)

• Powers with minimal commutator length in free products of groups