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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0323882-8
PII: S 0002-9947(1972)0323882-8
Keywords: Group ring, semisimplicity, solvable group
Article copyright: © Copyright 1972 American Mathematical Society