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A Dual View of the Clifford Theory of Characters of Finite Groups

Published online by Cambridge University Press:  20 November 2018

Richard L. Roth
Richard L. Roth*
Affiliation:
University of Colorado, Boulder, Colorado
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Let G be a finite group, K a normal subgroup of G, χ an irreducible complex character of G. In the usual decomposition of χ|κ, using Clifford's theorems, G/K is seen to operate by conjugation on the irreducible characters of K and if σ is an irreducible component of χ|κ, then I(σ) the inertial group of σ, plays an essential role as an appropriate intermediate subgroup for the analysis. In this paper we consider the case where G/K is abelian and study the action of the dual group (G/K)^ (of linear characters of G/K) on the irreducible characters of G effected by multiplication. This action appears to be related in a dual way to the action of G/K on the characters of K. We define a subgroup J(χ) of G which plays a role similar to that of I (σ) and which we call the dual inertial group of χ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 5 , October 1971 , pp. 857 - 865
Copyright
Copyright © Canadian Mathematical Society 1971

References

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