Finite groups with real-valued irreducible characters of prime degree.
Let \(G\) be a finite group and \(\text{cd}_{\text{rv}}(G)\) be the degrees of all the real-valued irreducible characters of \(G\). The authors prove the following: If every real-valued nonlinear irreducible character of \(G\) has prime degree then -- \(G\) is solvable. -- \(\text{cd}_{\text{rv}}(G)\subseteq\{1,2,p\}\), where \(p\) is an odd prime. -- \(l_2(G)\leqslant 2\) and \(l_{2'}(G)\leqslant 1\). They also consider the more general situation in which the real-valued irreducible characters of a finite group have all squarefree degree.
scientific article; zbMATH DE number 5355735