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 $G$.

AMS Subject Classification (1991): 16S34, 16U60

Keyword(s): group ring, involution

Received July 22, 2012, and in revised form August 7, 2013. (Registered under 54/2012.)