The cellular structure of the classifying spaces of finite groups

TL;DR

This paper fully characterizes the cellular structure of classifying spaces of finite groups with respect to prime p, using p-fusion analysis and Chachólski's approximation techniques.

Contribution

It completes the description of the $B\mathbb{Z}/p$-cellularization for all finite groups and primes, advancing understanding of their topological and algebraic structures.

Findings

Complete description of $B\mathbb{Z}/p$-cellularization for all finite groups

Analysis of p-fusion structures and strongly closed subgroups

Application of Chachólski's $A$-cellular approximation method

Abstract

In this paper we complete the description of the $B\mathbb{Z} /p$-cellularization of the classifying spaces of all finite groups, for all primes $p$. The techniques are based in a careful analysis of the $p$-fusion structure of the groups involved -with special attention to their strongly closed subgroups- and Chach\'olski's description of the $A$-cellular approximation.