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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $ 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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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1045598-2
PII: S 0002-9939(1991)1045598-2
Article copyright: © Copyright 1991 American Mathematical Society