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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

REFERENCES

1.Artin, E., Nesbitt, C. J. and Thrall, R. M., Rings with minimum condition (Ann Arbor, 1944).Google Scholar
2.Brauer, R. and Nesbitt, C., On the modular characters of groups, Ann. of Math. 42 (1941), 556–590.CrossRefGoogle Scholar
3.Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (New York, 1962).Google Scholar
4.Hall, M., The theory of groups (New York, 1959).Google Scholar
5.Osima, M., Note on the Kronecker product representations of a group, Proceedings of the Imperial Academy of Tokyo 17 (1941), 411–413.Google Scholar
6.Wallace, D. A. R., Note on the radical of a group algebra, Proc. Cambridge Philos. Soc. 54 (1958), 128–130.CrossRefGoogle Scholar
7.Wallace, D. A. R., Group algebras with central radicals, Proc. Glasgow Math. Assoc. 5 (1962), 103–108.CrossRefGoogle Scholar
8.Wallace, D. A. R., Group algebras with radicals of square zero, Proc. Glasgow Math. Assoc. 5 (1962), 158–159.CrossRefGoogle Scholar