Degrees of exceptional characters of certain finite groups

Author:
Harvey I. Blau

Journal:
Trans. Amer. Math. Soc. **249** (1979), 85-96

MSC:
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9947-1979-0526311-0

MathSciNet review:
526311

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Abstract: Let *G* be a finite group whose order is divisible by a prime *p* to the first power only. Restrictions beyond the known congruences modulo *p* are shown to hold for the degrees of the exceptional characters of *G*, under the assumptions that either all -elements centralizing a Sylow *p*-subgroup are in fact central in *G* and there are at least three conjugacy classes of elements of order *p*, or that the characters in question lie in the principal *p*-block. Results of Feit and the author are thereby generalized.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0526311-0

Keywords:
Ordinary character,
exceptional character,
modular representation,
cyclic Sylow subgroup,
symmetric and skew decomposition,
principal block

Article copyright:
© Copyright 1979
American Mathematical Society