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Group Algebras With Central Radicals

Published online by Cambridge University Press:  18 May 2009

D. A. R. Wallace
D. A. R. Wallace
Affiliation:
The University, Glasgow
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It is well known that when the characteristic p(≠ 0) of a field divides the order of a finite group, the group algebra possesses a non-trivial radical and that, if p does not divide the order of the group, the group algebra is semi-simple. A group algebra has a centre, a basis for which consists of the class-sums. The radical may be contained in this centre; we obtain necessary and sufficient conditions for this to happen.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 3 , January 1962 , pp. 103 - 108
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

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