Real characters of \(p'\)-degree.
The authors prove the following theorems using the Glauberman correspondence and the classification of simple groups: Theorem A. Let \(G\) be a finite group and suppose that \(p\neq 3\) is prime. If \(G\) is nonsolvable, then it has a nonprincipal, real, irreducible character of \(p'\)-degree. If \(G\) is solvable, then it has such a character if and only if \(|N_G(P)|\) is even, where \(P\in\text{Syl}_p(G)\). Theorem B. Suppose that \(G\) is a finite \(p\)-solvable group, where \(p\) is prime. Then \(G\) has a nonprincipal, real-valued, irreducible character of \(p'\)-degree if and only if \(|N_G(P)|\) is even, where \(P\in\text{Syl}_p(G)\).
scientific article; zbMATH DE number 2105346