Unit groups of completed modular group algebras and the isomorphism problem
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- by Frank Röhl PDF
- 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 $G$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 611-618
- MSC: Primary 16U60; Secondary 16W10, 16W50, 20C05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1045598-2
- MathSciNet review: 1045598