On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups

TL;DR

This paper proves that elementary amenable groups with bounded finite subgroup orders have a finite-dimensional classifying space for virtually cyclic subgroups, advancing understanding of their geometric and algebraic properties.

Contribution

It establishes the existence of finite-dimensional models for classifying spaces with virtually cyclic isotropy in elementary amenable groups with bounded finite subgroups.

Findings

Elementary amenable groups admit finite-dimensional classifying spaces for virtually cyclic subgroups.

Bounded orders of finite subgroups are sufficient for such models to exist.

The result applies to a broad class of groups with implications for geometric group theory.

Abstract

We show that elementary amenable groups, which have a bound on the orders of their finite subgroups, admit a finite dimensional model for the classifying space with virtually cyclic isotropy.