Degrees of exceptional characters of certain finite groups

Blau, Harvey I.

doi:10.1090/S0002-9947-1979-0526311-0

Degrees of exceptional characters of certain finite groups
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Trans. Amer. Math. Soc. 249 (1979), 85-96 Request permission

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 $p’$-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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