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On the commutativity of the radical of a group algebra

Published online by Cambridge University Press:  18 May 2009

D. A. R. Wallace
D. A. R. Wallace
Affiliation:
University of Glasgow, Glasgow, W.2
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Over a field of prime characteristic p the group algebra of a finite group has a non-trivial radical if and only if the order of the group is divisible by the prime p. In two earlier papers [7,8] we have imposed certain restrictions on the radical, namely that the radical be contained in the centre of the group algebra and that the radical be of square zero, and we have considered what influence these conditions have on the structure of the group itself. These conditions are, at first sight, of different types and our present paper is an attempt to generalise them by merely assuming that the radical is commutative.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 1 , January 1965 , pp. 1 - 8
Copyright
Copyright © Glasgow Mathematical Journal Trust 1965

References

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