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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Degrees of irreducible characters and normal $ p$-complements


Author: Ya. G. Berkovich
Journal: Proc. Amer. Math. Soc. 106 (1989), 33-35
MSC: Primary 20C15
MathSciNet review: 952314
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Abstract: John Tate [1] proved that if $ P \in {\mathbf{S}}{\text{y}}{{\text{l}}_p}(G)$, $ H$ is a normal subgroup of a finite group $ G$ and $ P \cap H \leq \Phi (P)$ ( $ \Phi (G)$ is the Frattini subgroup of $ G$) then $ H$ has a normal $ p$-complement. We prove in this note that Tate's theorem has nice character-theoretic applications.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0952314-X
PII: S 0002-9939(1989)0952314-X
Article copyright: © Copyright 1989 American Mathematical Society