Geodesic
Coprime Group Actions Fixing All Nonlinear Irreducible Characters
Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 68-82

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

The main result of this paper is the following:Theorem A. Let H and N be finite groups with coprime orders andsuppose that H acts nontrivially on N via automorphisms. Assume that Hfixes every nonlinear irreducible character of N. Then the derived subgroup ofN is nilpotent and so N is solvable of nilpotent length≦ 2.Why might one be interested in a situation like this? There has been considerable interest in the question of what one can deduce about a group Gfrom a knowledge of the setcd(G) = {x(l)lx ∈ Irr(G) }of irreducible character degrees of G.Recently, attention has been focused on the prime divisors of the elements of cd(G). For instance, in [9], O. Manz and R. Staszewski consider π-separable groups (for some set π of primes) with the property that every element of cd(G) is either a 77-number or a π'-number. 
Isaacs, I. M. Coprime Group Actions Fixing All Nonlinear Irreducible Characters. Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 68-82. doi: 10.4153/CJM-1989-003-2
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