Skip to main content
Log in

On weakly quasi-primitive characters of solvable groups

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

We define weakly quasi-primitive characters of solvable groups as a generalization of quasi-primitive characters, and present three main results about the zeros and the values for these characters, which in turn strengthen the corresponding theorems for quasi-primitive characters due to G. Navarro and T. Wilde.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Isaacs, I.M.: Characters of solvable and symplectic groups. Am. J. Math. 95, 594–635 (1973)

    Article  MathSciNet  Google Scholar 

  2. Isaacs, I.M.: Character Theory of Finite Groups. Academic Press, New York (1976)

    MATH  Google Scholar 

  3. Isaacs, I.M.: Characters of \(\pi \)-separable groups. J. Algebra 86, 98–128 (1984)

    Article  MathSciNet  Google Scholar 

  4. Isaacs, I.M.: Fong characters in \(\pi \)-separable groups. J. Algebra 99, 89–107 (1986)

    Article  MathSciNet  Google Scholar 

  5. Isaacs, I.M.: Partial characters of \(\pi \)-separable groups. In: Michler, G.O., Ringel, C.M. (eds.) Progress in Mathematics, vol. 95, pp. 273–287. Birkhäuser Verlag, Basel (1991)

    Google Scholar 

  6. Navarro, G.: Characters and Blocks of Finite Groups. Cambridge University Press, Cambridge (1998)

    Book  Google Scholar 

  7. Navarro, G.: Zeros of primitive characters in solvable groups. J. Algebra 221, 644–650 (1999)

    Article  MathSciNet  Google Scholar 

  8. Navarro, G.: Induction of characters and \(p\)-subgroups. J. Algebra 221, 217–228 (2002)

    Article  MathSciNet  Google Scholar 

  9. Wilde, T.: Primitive characters and permutation characters of solvable groups, preprint (2008). arXiv:0709.1209v2

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ping Jin.

Additional information

The second author was supported by the NSF of China (No. 11671238) and the NSF of Shanxi Province (No. 201601D011006).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, H., Jin, P. On weakly quasi-primitive characters of solvable groups. Arch. Math. 111, 561–568 (2018). https://doi.org/10.1007/s00013-018-1212-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-018-1212-y

Mathematics Subject Classification

Keywords

Navigation