Accessible characters are monomial
The following theorem is proved: Let G be a solvable finite group, \(N\trianglelefteq G\), \(\chi\in Irr(G)\), \(\chi =\sum_{i}z_ i\lambda_ i^{G}\), \((z_ i\in {\mathbb{Z}})\), the \(\lambda_ i^{G}\) induced from linear characters \(\lambda_ i\) of subnormal subgroups of N. Then \(\chi =\nu^{G}\) is induced from a linear character \(\nu\) of some subnormal subgroup of N. This theorem shows that for such non-principal \(\chi\) Artin's conjecture about holomorphic L-series is true. For these \(\chi\), written in the form \(\chi =\sum_{i}z_ i\lambda_ i^{G}\), \((z_ i\in {\mathbb{Z}})\), this was shown by J. Arthur and L. Clozel by means of some considerable effort [see: \textit{L. Clozel}, Base change for GL(n), in Proc. Int. Congr. Math. 1986 (1987)].
scientific article; zbMATH DE number 4061483