Unitary Subgroups of Commutative Group Algebras of the Characteristic Two

Let FG be the group algebra of a finite 2-group G over a finite field F of characteristic two and let ⊛ be an involution that arises from G. The ⊛-unitary subgroup of FG is denoted by V_⊛(FG) and defined as the set of all normalized units u satisfying the property u^⊛ = u⁻¹. We establish the order of V_⊛(FG) for all involutions ⊛ arising from G, where G is a finite cyclic 2-group, and show that all ⊛-unitary subgroups of FG are not isomorphic.