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Correspondences of Characters for Relatively Prime Operator Groups

Published online by Cambridge University Press:  20 November 2018

George Glauberman
George Glauberman*
Affiliation:
University of Chicago, Chicago, Illinois
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Let G be a finite group and let A be a finite solvable operator group on G. Suppose that A and G have relatively prime orders. Let T be the fixed-point subgroup of G with respect to A. We say that A fixes a complex character ζ of G if ζ (gα) = ζ (g) for all g ∈ G and α ϵ A. Our aim in this paper is to define a one-to-one correspondence between the irreducible characters of T and those irreducible characters of G that are fixed by A, and to prove some properties of this correspondence that were mentioned in (8).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1465 - 1488
Copyright
Copyright © Canadian Mathematical Society 1968

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