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Proceedings of the American Mathematical Society

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

 

 

An inequality for complex linear groups of small degree


Author: Harvey I. Blau
Journal: Proc. Amer. Math. Soc. 28 (1971), 405-408
MSC: Primary 20.75
DOI: https://doi.org/10.1090/S0002-9939-1971-0274601-X
MathSciNet review: 0274601
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Abstract: Let $ G$ be a finite complex irreducible linear group of degree less than $ p-1$ for some fixed prime $ p$, whose order is divisible by $ p$ to the first power only, and which has no normal Sylow $ p$-subgroup. An inequality of Brauer, which bounds $ p$ by a function of the number of conjugate classes of $ p$-elements, is improved.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0274601-X
Keywords: Faithful irreducible complex representation, complex character, prime order Sylow subgroup, small degree, conjugate class of $ p$-elements
Article copyright: © Copyright 1971 American Mathematical Society