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

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.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
College mathematics
Counterexamples
Mathematical theorems
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Zusammenfassung: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].
ISSN:0002-9939
1088-6826
DOI:10.2307/2046262