A Note on a Bound of Adan-Bante - Chen, Xiaoyou (Ukrains’kyi Matematychnyi Zhurnal, 2014)
Let G be a finite solvable group and let χ be a nonlinear irreducible (complex) character of G. Also let \( η \) (χ) be the number of nonprincipal irreducible constituents of \( \) , where \( \) denotes the complex conjugate of χ. Adan-Bante proved that there exist constants C and D such that dl (G/ ker χ) ≤ C \( η \) (χ) +D. In the present work, we establish a bound lower than the Adan-Bante bound for \( η \) (χ) > 2