Unit groups of completed modular group algebras and the isomorphism problem

Röhl, Frank

doi:10.1090/S0002-9939-1991-1045598-2

Unit groups of completed modular group algebras and the isomorphism problem
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Proc. Amer. Math. Soc. 111 (1991), 611-618 Request permission

Abstract:

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 $G$.

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