A periodicity theorem for acylindrically hyperbolic groups

Abstract

We generalize a well known periodicity lemma from the case of free groups to the case of acylindrically hyperbolic groups. This generalization will be used later to describe solutions of certain equations in acylindrically hyperbolic groups and to characterize verbally closed finitely generated acylindrically hyperbolic subgroups of finitely presented groups.

17 pages, 5 figures. New: We proved that the function $f(r)$ in the main theorem is linear. Introduction is improved. arXiv admin note: text overlap with arXiv:1805.08071