Geodesic
A Dual View of the Clifford Theory of Characters of Finite Groups
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 857-865

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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. 
Roth, Richard L. A Dual View of the Clifford Theory of Characters of Finite Groups. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 857-865. doi: 10.4153/CJM-1971-096-6
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