Involutions and unitary subgroups in group algebras

Abstract

Let FG be the group algebra of a finite group G over a field F of characteristic p. We give the maximal number of the non-isomorphic unitary subgroups with respect to the involutions of FG which arise from G. Furthermore, we characterize the group algebras with Hamiltonian unitary subgroup under the canonical involution, where G is a finite p-group and F is a finite field of characteristic p. Let FG denote the group algebra of a non-abelian group of order 8 over a finite field of characteristic two. We also describe the structure of the non-isomorphic unitary subgroups of FG linked to all the involutions which arise from G.