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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Degrees of exceptional characters of certain finite groups


Author: Harvey I. Blau
Journal: Trans. Amer. Math. Soc. 249 (1979), 85-96
MSC: Primary 20C15
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 $ 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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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