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
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E. Adan-Bante, “Products of characters and derived length,” J. Algebra, 266, 305–319 (2003).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 7, pp. 1006–1008, July, 2014.
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Chen, X. A Note on a Bound of Adan-Bante. Ukr Math J 66, 1126–1129 (2014). https://doi.org/10.1007/s11253-014-0987-7
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DOI: https://doi.org/10.1007/s11253-014-0987-7