On a theorem of Broline
The following addition to Broline's Theorem is given [see \textit{I. M. Isaacs}, Character theory of finite groups, New York, Academic Press (1976; Zbl 0337.20005), Theorem 12.24]: Theorem. Let \(\chi\) be an irreducible character of a finite group \(G\), \(\ker(\chi)\leq F\vartriangleleft G\) such that \(F/\ker(\chi)\) is nilpotent. If \((|F:\ker(\chi)|,\chi(1))=1\) and \(F\) is nonnilpotent, then there exists \(\psi\in\text{Irr}(G)\) such that \(\psi(1)>\chi(1)\) and \(\ker(\psi)<\ker(\chi)\).
scientific article; zbMATH DE number 1247583