Abstract
Over a field of 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. It would be of interest to determine the powers of the radical in the non-semi-simple case [2, p. 61]. In the particular case of p-groups the solution to the problem is known through the work of Jennings [6]. We here consider the special case of group algebras whose radicals have square zero and we relate this condition to the structure of the group itself.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference7 articles.
1. The structure of the group ring of a p-group over a modular field;Jennings;Trans. Amer. Math. Soc.,1941
2. On the Regular Representations of Algebras
3. Note on the Kronecker product of representations of a group
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