Representations of the Double Burnside Algebra and Cohomology of the Extraspecial p-Group

TL;DR

This paper investigates the structure of the mod p cohomology of certain summands in the stable splitting of the classifying space of an extraspecial p-group, providing new insights into its algebraic and topological properties.

Contribution

It determines the mod p cohomology of summands in the stable splitting of the p-completed classifying space of an extraspecial p-group, advancing understanding of its algebraic topology.

Findings

Identified the cohomology of summands in the stable splitting of BE

Provided explicit descriptions of the cohomology algebra structure

Enhanced understanding of the algebraic topology of extraspecial p-groups

Abstract

Let E be the extraspecial p-group of order p^3 and exponent p where p is an odd prime. We determine the mod p cohomology of summands in the stable splitting of p-completed classifying space BE modulo nilpotence.