Isomorphism problem of Unitary Subgroups of Group Algebras

Abstract

Let V * (F G) be the normalized unitary subgroup of the modular group algebra F G of a finite p-group G over a finite field F with the classical involution * . We investigate the isomorphism problem for the group V * (F G), that asks when the group V * (F G) is determined by its group algebra F G. We confirm it for classes of finite abelian p-groups, 2-groups of maximal class and non-abelian 2-groups of order at most 16.