Height of exceptional character degrees

Sibley, David A.

doi:10.1090/S0002-9939-1978-0466286-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Height of exceptional character degrees
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by David A. Sibley

Proc. Amer. Math. Soc. 69 (1978), 16-18

DOI: https://doi.org/10.1090/S0002-9939-1978-0466286-0

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Abstract:

Suppose a finite group G has an abelian Sylow p-group P which is a T.I. set and whose normalizer is a Frobenius group with kernel P. It is shown that the degree of an exceptional character of G is not divisible by p. That is, exceptional characters have height 0 in the principal p-block of G.

References

David A. Sibley, Finite linear groups with a strongly self-centralizing Sylow group. I, II, J. Algebra 36 (1975), no. 1, 158–166; ibid. 36 (1975), no. 2, 319–332. MR 382421, DOI 10.1016/0021-8693(75)90162-3