Chern classes and extraspecial groups

TL;DR

This paper investigates the structure of the mod-p cohomology ring of certain extraspecial p-groups, focusing on Chern classes and their algebraic relations, revealing polynomial subrings and their interactions.

Contribution

It analyzes the subquotient generated by Chern classes modulo the nilradical and explores the relations between Chern classes of one-dimensional and faithful irreducible representations.

Findings

The subring generated by Chern classes of faithful irreducible representations is polynomial.

Relations between different families of Chern class generators are established.

The structure of the subquotient ch(G) is characterized in terms of these generators.

Abstract

The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p. We investigate the subquotient ch(G) generated by Chern classes modulo the nilradical. The subring of ch(G) generated by Chern classes of one-dimensional representations was studied by Tezuka and Yagita. The subring generated by the Chern classes of the faithful irreducible representations is a polynomial algebra. We study the interplay between these two families of generators, and obtain some relations between them.