On unitary subgroups of group algebras

Let FG be the group algebra of a nite p-group G over a niteeld F of characteristic p and let * be the classical involution of FG. The *-unitary subgroup of FG, denoted by V*(FG), is de ned 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 noncommutative group algebras. A variant of the modular isomorphism question of group algebras is also considered.