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 circle star be an involution that arises from G. The circle star-unitary subgroup of FG is denoted by V circle star(FG) and defined as the set of all normalized units u satisfying the property u circle star = u-1. We establish the order of V circle star(FG) for all involutions circle star arising from G, where G is a finite cyclic 2-group, and show that all circle star-unitary subgroups of FG are not isomorphic.