Stable splitting and cohomology of p-local finite groups over the extraspecial p-group of order p^3 and exponent p

TL;DR

This paper investigates the cohomology and stable splitting of the p-complete classifying space of p-local finite groups over a specific extraspecial p-group, providing insights into their topological and algebraic structure.

Contribution

It offers new results on the cohomology and stable splitting of classifying spaces for p-local finite groups over extraspecial p-groups of order p^3 and exponent p.

Findings

Determined the cohomology structure of BG.

Described the stable splitting of BG.

Analyzed the implications for p-local finite groups.

Abstract

Let p be an odd prime. Let G be a p-local finite group over the extraspecial p-group p_+^{1+2}. In this paper we study the cohomology and the stable splitting of their p-complete classifying space BG.