Geodesic
Correspondences of Characters for Relatively Prime Operator Groups
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1465-1488

Voir la notice de l'article provenant de la source Cambridge University Press

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 (g α) = 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). 
Glauberman, George. Correspondences of Characters for Relatively Prime Operator Groups. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1465-1488. doi: 10.4153/CJM-1968-148-x
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