A cohomological characterization of locally virtually cyclic groups

TL;DR

This paper characterizes countable groups that are locally virtually cyclic using Bredon cohomological dimension, establishing a precise cohomological criterion for this class of groups.

Contribution

It provides a cohomological characterization of locally virtually cyclic groups, linking group structure with Bredon cohomology.

Findings

Countable groups are locally virtually cyclic iff their Bredon cohomological dimension for virtually cyclic subgroups is ≤ 1.

Establishes a new criterion connecting group theory and cohomology.

Advances understanding of the structure of virtually cyclic groups.

Abstract

We show that a countable group is locally virtually cyclic if and only if its Bredon cohomological dimension for the family of virtually cyclic subgroups is at most one.