Feit numbers and \(p'\)-degree characters
Let \(G\) be a finite group and \(X\) an irreducible character of \(G\). The Feit number of \(X\) is the smallest integer \(n\) such that the field of values of \(X\) is contained in the \(n\)th cylotomic field \(Q_n\). The Feit conjecture states that if \(G\) is a finite group and \(X\) is an irreducible character of \(G\) there is a \(g\) in \(G\) whose order is the Feit number of \(X\). The conjecture is still open, but it is proved for solvable groups by \textit{G. Amit} and \textit{D. Chillag} in [Pac. J. Math. 122, 257--261 (1986; Zbl 0558.20008)]. In the paper under review, the author shows: NEWLINENEWLINENEWLINELet \(G\) be a finite solvable group and \(p\) be a prime number and \(X\) be an irreducible character of \(G\) with odd degree. Then there exists an element g in \(N_G(P) /_P'\) whose order equals the Feit number of \(X\), where \(P\) is a Sylow \(p\)-subgroup of \(G\).
scientific article; zbMATH DE number 6648181