Unit groups of completed modular group algebras and the isomorphism problem

Author:
Frank Röhl

Journal:
Proc. Amer. Math. Soc. **111** (1991), 611-618

MSC:
Primary 16U60; Secondary 16W10, 16W50, 20C05

MathSciNet review:
1045598

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Abstract: In this paper it is shown that isomorphism of group algebras of finite -groups over the field of 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--algebra of the group of normalized units of the Magnus algebra of being a residually 'nilpotent -group of bounded exponent', is a split extension of the one associated to .

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1045598-2

Article copyright:
© Copyright 1991
American Mathematical Society