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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The kernel of a block of a group algebra


Author: Gerhard O. Michler
Journal: Proc. Amer. Math. Soc. 37 (1973), 47-49
MSC: Primary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1973-0310048-7
MathSciNet review: 0310048
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Abstract: Avoiding the theory of characters of finite groups and group algebras over fields of characteristic zero a ring theoretical proof is given for R. Brauer's theorem which asserts that the (modular) kernel of a block of a group algebra FG of a finite group over a field F of characteristic $ p > 0$ is a p-nilpotent normal subgroup of G.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310048-7
Keywords: Group algebra, block, modular irreducible representation, kernel of a block, Jacobson-radical, irreducible module, p-nilpotent groups
Article copyright: © Copyright 1973 American Mathematical Society