Skip to main content
SpringerLink
Log in

On the structure of p-schemes

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We introduce and study an analog of p-groups in general scheme theory. It is proved that a scheme C is a p-scheme if and only if so is each homogeneous component of C. Moreover, the automorphism group of a p-scheme is a p-group, and the 2-orbit scheme of a permutation group G is a p-scheme if and only if G is a p-group. Both of these assertions follow from the fact that the class of p-schemes is closed with respect to extensions. Bibliography: 9 titles.

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. S. Evdokimov, M. Karpinski, and I. Ponomarenko, “On a new high dimensional Weisfeiler-Leman algorithm,” J. Algebraic Combin., 10, 29–45 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Evdokimov and I. Ponomarenko, “Separability number and Schurity number of coherent configurations,” Electron. J. Combin., 7, #R31 (2000).

    Google Scholar 

  3. I. A. Faradžev, M. H. Klin, and M. E. Muzychuk, “Cellular rings and groups of automorphisms of graphs,” in: I. A. Faradžev et al. (eds.), Investigations in Algebraic Theory of Combinatorial Objects, Kluwer Acad. Publ., Dordrecht (1994), pp. 1–152.

    Google Scholar 

  4. D. G. Higman, “Coherent configurations,” Geom. Dedicata, 4, 1–32 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Klin, M. Muzychuk, C. Pech, A. Woldar, and P.-H. Zieschang, “Association schemes on 28 points as mergings of a half-homogeneous coherent configuration,” European J. Combin., 28, 1994–2025 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  6. I. Ponomarenko, “Cellular algebras and graph isomorphism problem,” Research Report No. 8592-CS, University of Bonn, April 1993.

  7. B. Weisfeiler (ed.), On Construction and Identification of Graphs, Springer Lect. Notes, Vol. 558. Springer-Verlag, Berlin (1976).

    MATH  Google Scholar 

  8. P.-H. Zieschang, An Algebraic Approach to Association Schemes, Springer-Verlag, Berlin (1996).

    MATH  Google Scholar 

  9. P.-H. Zieschang, Theory of Association Schemes, Springer-Verlag, Berlin (2005).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    I. N. Ponomarenko

  2. Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

    A. Rahnamai Barghi

Authors
  1. I. N. Ponomarenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Rahnamai Barghi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. N. Ponomarenko.

Additional information

__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 190–202.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ponomarenko, I.N., Rahnamai Barghi, A. On the structure of p-schemes. J Math Sci 147, 7227–7233 (2007). https://doi.org/10.1007/s10958-007-0539-x

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-007-0539-x

Keywords

Search

Navigation