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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Authors: Gail L. Carns and Chong-yun Chao
Journal: Proc. Amer. Math. Soc. 33 (1972), 323-328
MSC: Primary 20C05
MathSciNet review: 0294521
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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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DOI: https://doi.org/10.1090/S0002-9939-1972-0294521-5
Keywords: Modular group algebra, radical, annihilator, center, dimension, maximal subgroups, conjugate classes, Frattini subalgebra, nonimbedding, outer automorphism
Article copyright: © Copyright 1972 American Mathematical Society