Unitary Subgroups of commutative group algebras of characteristic two

Abstract

Let F G be the group algebra of a finite 2-group G over a finite field F of characteristic two and ⊛ an involution which arises from G. The ⊛-unitary subgroup of F G, denoted by V ⊛ (F G), is defined to be the set of all normalized units u satisfying the property u ⊛ = u −1 . In this paper we establish the order of V ⊛ (F G) for all involutions ⊛ which arise from G, where G is a finite cyclic 2-group and show that all ⊛-unitary subgroups of F G are not isomorphic.