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

 

Minimal degrees of faithful characters of finite groups with a T.I. Sylow $ p$-subgroup


Authors: T. R. Berger, P. Landrock and G. O. Michler
Journal: Proc. Amer. Math. Soc. 99 (1987), 15-21
MSC: Primary 20C15
MathSciNet review: 866421
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Abstract: Using the classification of the finite simple groups we show in this article that a faithful complex character $ \chi $ of a finite group $ G$ with a nonnormal T.I. Sylow $ p$-subgroup $ P$ has degree $ \chi (1){\text{ > }}\sqrt {\left\vert P \right\vert} - 1$. This result verifies a conjecture of H. S. Leonard [10].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866421-1
PII: S 0002-9939(1987)0866421-1
Article copyright: © Copyright 1987 American Mathematical Society