Chow ring and BP-theory of the extraspecial 2-group of order 32

TL;DR

This paper computes the mod 2 Chow ring of the classifying space of a specific extraspecial 2-group of order 32, revealing the presence of nilpotent elements.

Contribution

It explicitly determines the Chow ring structure for the classifying space of the extraspecial 2-group of order 32, a novel calculation in algebraic topology.

Findings

Chow ring contains nilpotent elements.

Explicit description of the mod 2 Chow ring.

Analysis of the classifying space of the extraspecial 2-group.

Abstract

We write down the mod 2 Chow ring of the classifying space of the central product of two dihedral groups of order 8. This Chow ring has nilpotent elements.