Skip to main content
SpringerLink
Log in

A new characterization for some linear groups

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

Let G be a group and π e (G) be the set of element orders of G. Let \({k\in\pi_e(G)}\) and m k be the number of elements of order k in G. Let \({{\rm nse}(G) = \{m_k|k\in\pi_e(G)\}}\) . In Shen et al. (Monatsh Math, 2009), the authors proved that \({A_4\cong {\rm PSL}(2, 3), A_5\cong \rm{PSL}(2, 4)\cong \rm{PSL}(2,5)}\) and \({A_6\cong \rm{PSL}(2,9)}\) are uniquely determined by nse(G). In this paper, we prove that if G is a group such that nse(G) = nse(PSL(2, q)), where \({q\in\{7,8,11,13\}}\) , then \({G\cong {PSL}(2,q)}\) .

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. Brandl R., Shi W.J.: The characterization of PSL2(q) by its element orders. J. Algebra 163, 109–114 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Frobenius, G.: Verallgemeinerung des sylowschen satze. Berliner sitz, pp. 981–993 (1895)

  3. Hall M.: The Theory of Groups. Macmillan, New York (1959)

    MATH  Google Scholar 

  4. Herzog M.: On finite simple groups of order divisble by three primes only. J. Algebra 10, 383–388 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  5. Khosravi A., Khosravi B.: 2-Recognizability by prime graph of PSL(2, p 2). Sib. Math. J. 49, 749–757 (2008)

    Article  MathSciNet  Google Scholar 

  6. Khosravi B., Khosravi B., Khosravi B.: On the prime graph of PSL(2, p) where p > 3 is a prime number. Acta. Math. Hung. 116, 295–307 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Khosravi B.: n-Recognition by prime graph of the simple group PSL(2, q). J. Algebra Appl. 7, 735–748 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Miller G.: Addition to a theorem due to Frobenius. Bull. Am. Math. Soc. 11, 6–7 (1904)

    Article  Google Scholar 

  9. Robinson D.J.S.: A Course in the Theory of Groups. Springer, New York (1982)

    MATH  Google Scholar 

  10. Shao C.G., Shi W.J., Jiang Q.H.: Characterization of simple K 4-groups. Front. Math. China 3, 355–370 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Shen, R., Shao, C., Jiang, Q., Shi, W., Mazurov, V.: A new characterization of A 5. Monatsh. Math. (2009, to appear)

  12. The GAP Group, GAP—Groups, Algorithms and Programming, Vers. 4.4.12 (2008). http://www.gap-system.org

Download references

Author information

Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., 15914, Tehran, Iran

    Maryam Khatami, Behrooz Khosravi & Zeinab Akhlaghi

Authors
  1. Maryam Khatami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Behrooz Khosravi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zeinab Akhlaghi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Behrooz Khosravi.

Additional information

Communicated by J. S. Wilson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khatami, M., Khosravi, B. & Akhlaghi, Z. A new characterization for some linear groups. Monatsh Math 163, 39–50 (2011). https://doi.org/10.1007/s00605-009-0168-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-009-0168-1

Keywords

Mathematics Subject Classification (2000)

Search

Navigation