Minimal Degrees of Faithful Characters of Finite Groups with a T.I. Sylow p-Subgroup

Using the classification of the finite simple groups we show in this article that a faithful complex character χ of a finite group G with a nonnormal T.I. Sylow p-subgroup P has degree$\chi(1) > \sqrt{|P|} - 1$. This result verifies a conjecture of H. S. Leonard [10].

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Veröffentlicht in:	Proceedings of the American Mathematical Society 1987-01, Vol.99 (1), p.15-21, Article 15
Hauptverfasser:	Berger, T. R., Landrock, P., Michler, G. O.
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Sprache:	eng
Schlagworte:	Algebra College mathematics Counterexamples Mathematical theorems
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description	Using the classification of the finite simple groups we show in this article that a faithful complex character χ of a finite group G with a nonnormal T.I. Sylow p-subgroup P has degree$\chi(1) > \sqrt{\|P\|} - 1$. This result verifies a conjecture of H. S. Leonard [10].
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subjects	Algebra College mathematics Counterexamples Mathematical theorems
title	Minimal Degrees of Faithful Characters of Finite Groups with a T.I. Sylow p-Subgroup
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