Skip to main content
SpringerLink
Log in

Conjecture of Li and Praeger concerning the isomorphisms of Cayley graphs of A5

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

LetG be a finite group, andS a subset ofG \ |1| withS =S −1. We useX = Cay(G,S) to denote the Cayley graph ofG with respect toS. We callS a Cl-subset ofG, if for any isomorphism Cay(G,S) ≈ Cay(G,T) there is an α∈ Aut(G) such thatS α =T. Assume that m is a positive integer.G is called anm-Cl-group if every subsetS ofG withS =S −1 and | S | ≤m is Cl. In this paper we prove that the alternating groupA 5 is a 4-Cl-group, which was a conjecture posed by Li and Praeger.

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. Li, C. H., Praeger, C. E., The finite simple groups with at most two fusion classes of every order, Comm. Algebra, 1996, 24: 3681–3704.

    Article  MATH  MathSciNet  Google Scholar 

  2. Sabidussi, G. O., Vertex-transitive graphs, Monash. Math., 1964, 68: 426–438.

    Article  MATH  MathSciNet  Google Scholar 

  3. Xu, M. Y., Automorphism groups and isomolphisms of Cayley digraphs, Discrete Math., 1998, 182: 309–319.

    Article  MATH  MathSciNet  Google Scholar 

  4. Dixon, J. D., Mortimer, B., Permutation Groups, Berlin: Springer-Verlag, 1996.

    MATH  Google Scholar 

  5. Suzuki, M., Group Theory I, Berlin: Springer Verlag, 1982.

    MATH  Google Scholar 

  6. Wielandt, H., Finite Permutation Groups, New York: Academic Press, 1964.

    MATH  Google Scholar 

  7. Babai, L., Isomorphism problem for a class of point-symmetric structures, Acta Math. Acad. Sci. Hung., 1977, 29: 329–336.

    Article  MATH  MathSciNet  Google Scholar 

  8. Gorenstein, D., Finite Simple Groups, New York: Plenum Press, 1982.

    MATH  Google Scholar 

  9. Conway, J. H., Curtis, R. T., Norton, S. P. et al., An Atlas of Finite Groups, Oxford: Clarendon Press, 1985.

    Google Scholar 

  10. Kleidman, P., Liebeck, M., The Subgroup Stmcture of the Finite Classical Groups, Cambridge: Cambridge University Press, 1990.

    Google Scholar 

  11. Gu, Z. Y., Li, C. H., A nonabelian CI-group, Australas. J. Combin., 1998, 17: 229–233.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Xu Mingyao & Fang Xingui

  2. Division of Mathematical Sciences, Pukyong National University, 608-737, Pusan, Republic of Korea

    Sim Hyo-Seob & Baik Young-Gheel

Authors
  1. Xu Mingyao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fang Xingui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sim Hyo-Seob
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Baik Young-Gheel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fang Xingui.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, M., Fang, X., Sim, HS. et al. Conjecture of Li and Praeger concerning the isomorphisms of Cayley graphs of A5 . Sci. China Ser. A-Math. 44, 1502–1508 (2001). https://doi.org/10.1007/BF02880789

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02880789

Keywords

Search

Navigation