UNIT GROUPS OF COMPLETED MODULAR GROUP-ALGEBRAS AND THE ISOMORPHISM-PROBLEM

In this paper it is shown that isomorphism of group algebras of finite p-groups over the field of p elements implies isomorphism of the groups, if one of the groups has a normal complement in the group of normalized units of the group algebra. Furthermore, a class of groups satisfying this condition is provided, and it is shown that the associated graded Lie-p-algebra of the group of normalized units of the Magnus algebra of G, G being a residually 'nilpotent p-group of bounded exponent', is a split extension of the one associated to G.