On the radical of the group algebra of a 𝑝-group over a modular field

Carns, Gail L.; Chao, Chong-yun

doi:10.1090/S0002-9939-1972-0294521-5

On the radical of the group algebra of a $p$-group over a modular field
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by Gail L. Carns and Chong-yun Chao PDF

Proc. Amer. Math. Soc. 33 (1972), 323-328 Request permission

Abstract:

Let G be a finite p-group, K be the field of integers modulo p, KG be the group algebra of G over K and N be the radical of KG. By using the fact that the annihilator, $A(N)$, of N is one dimensional, we characterize the elements of $A({N^2})$. We also present relationships among the cardinality of $A({N^2})$, the number of maximal subgroups in G and the number of conjugate classes in G. Theorems concerning the Frattini subalgebra of N and the existence of an outer automorphism of N are also proved.

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