Unitary Subgroups of commutative group algebras of characteristic two

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

Categories: math.RA