2019
Том 71
№ 11

# Chen Xiaoyou

Articles: 1
Brief Communications (English)

### A Note on a Bound of Adan-Bante

Ukr. Mat. Zh. - 2014. - 66, № 7. - pp. 1006–1008

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