On the virtually-cyclic dimension of surface braid groups and right-angled Artin groups

TL;DR

This paper establishes bounds on the virtually-cyclic dimension for certain groups, including surface braid groups and right-angled Artin groups, based on their subgroup structures and properties.

Contribution

It provides new bounds for the virtually-cyclic dimension of surface braid groups and right-angled Artin groups, extending understanding of their geometric and algebraic properties.

Findings

Bound for virtually-cyclic dimension of surface braid groups with genus > 2

Bound for virtually-cyclic dimension of right-angled Artin groups

Application of subgroup containment properties to dimension bounds

Abstract

We give a bound for the virtually cyclic dimension of groups with a normal subgroup of finite index which satisfies that every infinite virtually-cyclic subgroup is contained in a unique maximal such subgroup. As an application we provide a bound for the virtually-cyclic dimension for the braid group of a closed surface with genus greater than 2 and for right-angled Artin groups.