Skip to main content
SpringerLink
Log in

Finite groups whose noncentral class sizes have the same p-part for some prime p

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We describe the structure of the finite groups in which the sizes of noncentral conjugacy classes have the same p-part, for some prime p. We prove that they are solvable, they have a normal p-complement and their Fitting length is at most three.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. R. Camina, Arithmetical conditions on the conjugacy class numbers of a finite group, Journal of the London Mathematical Society 5 (1972), 127–132.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Cossey and T. Hawkes, Sets of p-powers as conjugacy class sizes, Proceedings of the American Mathematical Society 128 (2000), 49–51.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Dolfi and M. S. Lucido, Finite groups in which p′-classes have q′-length, Israel Journal of Mathematics 122 (2001), 93–115.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Fernández-Alcober and A. Moretó, On the number of conjugacy class sizes and character degrees in finite p-groups, Proceedings of the American Mathematical Society 129 (2001), 3201–3204.

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967.

    Book  MATH  Google Scholar 

  6. B. Huppert, A remark on a theorem of J. G. Thompson, Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni 9 (1998), 145–148.

    MathSciNet  MATH  Google Scholar 

  7. I. M. Isaacs, Groups with many equal classes, Duke Mathematical Journal 37 (1970), 501–506.

    Article  MathSciNet  MATH  Google Scholar 

  8. I. M. Isaacs, Character Theory of Finite Groups, AMS Chelsea Publishing, Providence, RI, 2006.

    MATH  Google Scholar 

  9. I. M. Isaacs, Finite Group Theory, Graduate Studies in Mathematics 92, American Mathematical Society, Providence, RI, 2008.

    Google Scholar 

  10. I. M. Isaacs, Subgroups generated by small classes in finite groups, Proceedings of the American Mathematical Society 136 (2008), 2299–2301.

    Article  MathSciNet  MATH  Google Scholar 

  11. I. M. Isaacs and D. S. Passman, Half-transitive automorphism groups, Canadian Journal of Mathematics 18 (1966), 1243–1250.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Ishikawa, On finite p-groups which have only two conjugacy lengths, Israel Journal of Mathematics 129 (2002), 119–123.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. F. Riedl, Character degrees, class sizes, and normal subgroups of a certain class of p-groups, Journal of Algebra 218 (1999), 190–215.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. N. Ward, Automorphisms of finite groups and their fixed-point groups, Journal of the Australian Mathematical Society 9 (1969), 467–477.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica U. Dini, Università degli Studi di Firenze, viale Morgagni 67/A, 50134, Firenze, Italy

    Carlo Casolo & Silvio Dolfi

  2. Dipartimento di Matematica Applicata, Università Ca’Foscari, Dorsoduro 3825/E, 30123, Venezia, Italy

    Enrico Jabara

Authors
  1. Carlo Casolo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silvio Dolfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Enrico Jabara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carlo Casolo.

Additional information

The authors are partially supported by MIUR project “Teoria dei gruppi e applicazioni”.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Casolo, C., Dolfi, S. & Jabara, E. Finite groups whose noncentral class sizes have the same p-part for some prime p . Isr. J. Math. 192, 197–219 (2012). https://doi.org/10.1007/s11856-012-0022-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-012-0022-3

Keywords

Search

Navigation