COMMUTATOR LENGTH OF POWERS IN FREE PRODUCTS OF GROUPS

摘要

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