The verbal width of acylindrically hyperbolic groups is infinite

TL;DR

This paper proves that the verbal width, a measure of how elements can be expressed as products of certain words, is infinite in acylindrically hyperbolic groups, including hyperbolic groups, mapping class groups, and Out(Fn).

Contribution

It establishes the infinite verbal width property for a broad class of important groups, extending known results to acylindrically hyperbolic groups.

Findings

Verbal width is infinite in acylindrically hyperbolic groups.

Includes hyperbolic groups, mapping class groups, and Out(Fn).

Advances understanding of algebraic properties of these groups.

Abstract

We show that the verbal width is infinite for acylindrically hyperbolic groups, which include hyperbolic groups, mapping class groups and Out(Fn).