Actions and invariant character degrees (Q687665)

The main result of the paper is: Theorem A. Suppose the finite group \(S\) acts on the finite solvable group \(G\) coprimely and let \(H\) be an \(S\)- invariant \(\pi\)-complement. Then every \(S\)-invariant irreducible character of \(G\) has \(\pi\)-degree if and only if \(C_ G(S)\) normalizes \(H\) and \(C_ H(S)\) is an abelian complement of \([H,S]\) in \(H\). -- The Glauberman-Isaacs correspondence and character theory of fully ramified sections are needed for the proof.