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Transactions of the American Mathematical Society

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On the semisimplicity of group rings of solvable groups


Authors: C. R. Hampton and D. S. Passman
Journal: Trans. Amer. Math. Soc. 173 (1972), 289-301
MSC: Primary 20C05
MathSciNet review: 0323882
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Abstract: Let $ K[G]$ denote the group ring of $ G$ over the field $ K$ of characteristic $ p > 0$. An interesting unsolved problem is to find necessary and sufficient conditions on $ G$ for $ K[G]$ to be semisimple. Even the special case in which $ G$ is assumed to be a solvable group is still open. In this paper we prove a number of theorems which may be of use in this special case.


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

  • [1] D. S. Passman, On the semisimplicity of modular group algebras. II, Canad. J. Math. 21 (1969), 1137–1145. MR 0248245
  • [2] D. S. Passman, Radicals of twisted group rings. II, Proc. London Math. Soc. (3) 22 (1971), 633–651. MR 0292960
  • [3] Donald S. Passman, Infinite group rings, Marcel Dekker, Inc., New York, 1971. Pure and Applied Mathematics, 6. MR 0314951
  • [4] D. S. Passman, Some isolated subsets of infinite solvable groups, Pacific J. Math. 45 (1973), 313–319. MR 0323883
  • [5] A. E. Zalesskiĭ, On group rings of solvable groups , Izv. Akad. Nauk BSSR 2 (1970), 13-21. (Russian)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0323882-8
Keywords: Group ring, semisimplicity, solvable group
Article copyright: © Copyright 1972 American Mathematical Society