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

Berger, T. R.; Landrock, P.; Michler, G. O.

doi:10.1090/S0002-9939-1987-0866421-1

Minimal degrees of faithful characters of finite groups with a T.I. Sylow $p$-subgroup
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by T. R. Berger, P. Landrock and G. O. Michler PDF

Proc. Amer. Math. Soc. 99 (1987), 15-21 Request permission

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 $\chi (1){\text { > }}\sqrt {\left | P \right |} - 1$. This result verifies a conjecture of H. S. Leonard [10].

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