Quadratic forms in characteristic 2 and a Wedderburn decomposition over rationals

Abstract

Let F be a field of characteristic 2. In this paper, we provide an interesting application of quadratic forms over F in determination of the Wedderburn decomposition of the rational group algebra Q[G], where G is a real special 2-group. We further apply these computations to exhibit two non-isomorphic real special 2-groups with isomorphic rational group algebra.