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The Jacobson radical of the group algebra of a finite group


Author: Surinder Singh Bedi
Journal: Proc. Amer. Math. Soc. 75 (1979), 13-18
MSC: Primary 16A26; Secondary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1979-0529203-1
MathSciNet review: 529203
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Abstract: Let K be a field of characteristic $ p \ne 0$ and G a finite group such that $ p\vert o(G)$. Suppose G is a Frobenius group with a Sylow p-subgroup P as a complement. Then we have proved that

$\displaystyle JK(G) = \bigcap\limits_{x \in G} {JK({P^x})K(G).} $

We have given an example to show that equality does not hold in general.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0529203-1
Keywords: Group algebra, Jacobson radical, transitive permutation group, Frobenius group with p-Sylow subgroup as complement, Frobenius kernel, central ideal, semidirect product
Article copyright: © Copyright 1979 American Mathematical Society