TY - JOUR AU - Xiaoyou Chen PY - 2014/07/25 Y2 - 2024/03/28 TI - A Note on a Bound of Adan-Bante JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 66 IS - 7 SE - Short communications DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2195 AB - Let G be a finite solvable group and let χ be a nonlinear irreducible (complex) character of G. Also let \( \eta \) (χ) be the number of nonprincipal irreducible constituents of \( \upchi \overline{\upchi} \) , where \( \overline{\upchi} \) denotes the complex conjugate of χ. Adan-Bante proved that there exist constants C and D such that dl (G/ ker χ) ≤ C \( \eta \) (χ) +D. In the present work, we establish a bound lower than the Adan-Bante bound for \( \eta \) (χ) > 2 ER -