Abstract.
Let the finite solvable group A be acting on a finite group G and suppose that (|A|,|G|) = 1. The Glauberman correspondence provides a natural one-to-one correspondence between the irreducible characters of G invariant under A and all the irreducible characters of C G (A). Let cd(C G (A)) denote the set of degrees of the irreducible characters of C G (A) and let cd A (G) denote the set of degrees of the A-invariant irreducible characters of G. We prove that for every pair of positive integers (n, m), if m > 1, then there exists A and G as above such that \(|{\rm cd}({\rm C}_G(A))| = n\) and \( |{\rm cd}_A(G)| = m\).
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Received: 1.4.1997
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Turull, A. Centralizers and character degrees. Arch. Math. 74, 410–413 (2000). https://doi.org/10.1007/s000130050461
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DOI: https://doi.org/10.1007/s000130050461