Equivariant quadratic forms in characteristic 2

TL;DR

This paper determines the structure of the Witt group of equivariant quadratic forms over a finite field of characteristic 2, relating it to group invariants like 2-rank and self-dual modules.

Contribution

It provides an explicit isomorphism for the Witt group of equivariant quadratic forms in characteristic 2, connecting algebraic invariants of the group and module structure.

Findings

Witt group is an elementary abelian 2-group

Rank of the Witt group equals s + t

Explicit isomorphism described

Abstract

Let $G$ be a finite group and $K$ a finite field of characteristic $2$. Denote by $t$ the $2$-rank of the commutator factor group $G/G'$ and by $s$ the number of self-dual simple $KG$-modules. Then the Witt group of equivariant quadratic forms $\WQ (K,G)$ is isomorphic to an elementary abelian $2$-group of rank $s+t$.