Transfer and Chern classes for extraspecial p-groups

TL;DR

This paper investigates the structure of the cohomology ring of extraspecial p-groups, focusing on the subring generated by Chern classes and transfers, revealing its relation to the entire cohomology ring.

Contribution

It provides a new formula relating Chern classes to transfers and analyzes the subring generated by these elements within the cohomology ring.

Findings

The subring generated by Chern classes and transfers is larger than the Chern subring.

This subring does not encompass the entire cohomology ring, even modulo nilradical.

A formula relating Chern classes to transfers is established.

Abstract

In the cohomology ring of an extraspecial p-group, the subring generated by Chern classes and transfers is studied. This subring is strictly larger than the Chern subring, but still not the whole cohomology ring, even modulo nilradical. A formula is obtained relating Chern classes to transfers.