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Ukrainian Mathematical Journal

, Volume 66, Issue 7, pp 1126–1129 | Cite as

A Note on a Bound of Adan-Bante

  • Xiaoyou Chen
Article
  • 56 Downloads

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

Keywords

Complex Conjugate Nonnegative Integer Henan Province Education Department Vector Space Versus 
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References

  1. 1.
    E. Adan-Bante, “Products of characters and derived length,” J. Algebra, 266, 305–319 (2003).Google Scholar
  2. 2.
    E. Adan-Bante, “Products of characters with few irreducible constituents,” J. Algebra, 311, 38–68 (2007).Google Scholar
  3. 3.
    E. Adan-Bante, Products of Characters and Derived Length of Finite Solvable Groups, Ph. D. Thesis, University of Illinois, Urbana (2002).Google Scholar
  4. 4.
    T. M. Keller, “Orbit sizes and character degrees III,” J. Reine Angew. Math., 545, 1–17 (2002).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Xiaoyou Chen
    • 1
  1. 1.College of SciencesHenan University of TechnologyZhengzhouChina

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