A Note on a Bound of Adan-Bante

  • Xiaoyou Chen


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
How to Cite
Chen, X. “A Note on a Bound of Adan-Bante”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 7, July 2014, pp. 1006–1008, https://umj.imath.kiev.ua/index.php/umj/article/view/2195.
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