Skip to main content
SpringerLink
Log in

The order of elements in Sylow p-subgroups of the symmetric group

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

Define a random variable ξn by choosing a conjugacy class C of the Sylow p-subgroup of Spn by random, and let ξn be the logarithm of the order of an element in C. We show that ξn has bounded variance and mean order log n /log p +O(1), which differs greatly from the average order of elements chosen with equal probability.

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. M. Abért and B. Virág, Dimension and randomness in groups acting on rooted trees, to appear.

  2. P. Erdös and P. Turán, On some problems of a statistical group theory. I, Z. Wahr-scheinlichkeitstheorie und Verw. Gebiete, 4 (1965), 175-186.

    Article  MATH  Google Scholar 

  3. P. Erdös and P. Turán, On some problems of a statistical group theory. II, Acta Math. Acad. Sci. Hangar., 18 (1967), 151-163.

    Article  MATH  Google Scholar 

  4. P. Erdös and P. Turán, On some problems of a statistical group theory. III, Acta Math. Acad. Sci. Hangar., 18 (1967), 309-320.

    Article  MATH  Google Scholar 

  5. P. Erdös and P. Turán, On some problems of a statistical group theory. IV, Acta Math. Acad. Sci. Hangar., 19 (1968), 413-435.

    Article  MATH  Google Scholar 

  6. P. Erdös and P. Turán, On some problems of a statistical group theory. V, Period. Math. Hungar., 1 (1971), 5-13.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Erdös and P. Turán, On some problems of a statistical group theory. VI, J. Indian Math. Soc., 34 (1971), 175-192.

    MATH  Google Scholar 

  8. P. Erdös and P. Turán, On some problems of a statistical group theory. VII, Period. Math. Hungar., 2 (1972), 149-163.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. P. Pálfy and M. Szalay, The distribution of the character degrees of the symmetric p-groups, Acta Math. Hungar., 41 (1983), 137-150.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. P. Pálfy and M. Szalay, On a problem of P. Turán concerning Sylow subgroups, in: Studies in Pure Mathematics to the Memory of P. Turán, Birkhauser (Basel, 1983), pp. 531-542.

  11. P. P. Pálfy and M. Szalay, Further probabilistic results on the symmetric p-groups, Acta Math. Hangar., 53 (1989), 173-195.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut Eckerstr. 1, 79104, Freiburg, Germany E-mail

    Jan-Christoph Schlage-Puchta

Authors
  1. Jan-Christoph Schlage-Puchta
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schlage-Puchta, JC. The order of elements in Sylow p-subgroups of the symmetric group. Acta Mathematica Hungarica 105, 187–195 (2004). https://doi.org/10.1023/B:AMHU.0000049286.70907.fb

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:AMHU.0000049286.70907.fb

Search

Navigation