The Jacobson radical of the group algebra of a finite group
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- by Surinder Singh Bedi PDF
- Proc. Amer. Math. Soc. 75 (1979), 13-18 Request permission
Abstract:
Let K be a field of characteristic $p \ne 0$ and G a finite group such that $p|o(G)$. Suppose G is a Frobenius group with a Sylow p-subgroup P as a complement. Then we have proved that \[ JK(G) = \bigcap \limits _{x \in G} {JK({P^x})K(G).} \] We have given an example to show that equality does not hold in general.References
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- I. N. Herstein, Noncommutative rings, The Carus Mathematical Monographs, No. 15, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR 0227205
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
- Donald Passman, Permutation groups, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0237627
- Donald S. Passman, Infinite group rings, Pure and Applied Mathematics, vol. 6, Marcel Dekker, Inc., New York, 1971. MR 0314951
- Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
- D. A. R. Wallace, Group algebras with central radicals, Proc. Glasgow Math. Assoc. 5 (1962), 103–108 (1962). MR 140589
Additional Information
- © Copyright 1979 American Mathematical Society
- 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