ON UNITARY SUBGROUPS OF GROUP ALGEBRAS

Abstract

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and let $*$ be the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all normalized units $u$ satisfying the property $u^*=u^{-1}$. In this paper we give a recursive method how to compute the order of the $*$-unitary subgroup for certain non-commutative group algebras. A variant of the modular isomorphism question of group algebras is also considered.