Skip to main content
SpringerLink
Log in

Generating Triples of Involutions of Groups of Lie Type of Rank 2 Over Finite Fields

  • Published:
Algebra and Logic Aims and scope

For finite simple groups U5(2n), n > 1, U4(q), and S4(q), where q is a power of a prime p > 2, q − 1 ≠= 0(mod4), and q ≠= 3, we explicitly specify generating triples of involutions two of which commute. As a corollary, it is inferred that for the given simple groups, the minimum number of generating conjugate involutions, whose product equals 1, is equal to 5.

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. Ya. N. Nuzhin, “Generating triples of involutions for alternating groups,” Mat. Zametki, 51, No. 4, 91-95 (1992).

    MathSciNet  MATH  Google Scholar 

  2. Ya. N. Nuzhin, “Generating triples of involutions for Chevalley groups over a finite field of characteristic 2,” Algebra and Logic, 29, No. 2, 134-143 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  3. Ya. N. Nuzhin, “Generating triples of involutions for Lie-type groups over a finite field of odd characteristic. I,” Algebra and Logic, 36, No. 1, 46-59 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  4. Ya. N. Nuzhin, “Generating triples of involutions for Lie-type groups over a finite field of odd characteristic. II,” Algebra and Logic, 36, No. 4, 245-256 (1997).

  5. V. D. Mazurov, “On generation of sporadic simple groups by three involutions two of which commute,” Sib. Math. J., 44, No. 1, 160-164 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  6. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford (1985).

  7. Unsolved Problems in Group Theory, The Kourovka Notebook, No. 19, Institute of Mathematics SO RAN, Novosibirsk (2018); http://www.math.nsc.ru/∼alglog/19tkt.pdf.

  8. J. M. Ward, Generation of simple groups by conjugate involutions, PhD Thesis, Queen Mary college, Univ. London (2009).

  9. E. S. Rapaport, “Cayley color groups and Hamilton lines,” Scripta Math., 24, 51-58 (1959).

    MathSciNet  MATH  Google Scholar 

  10. I. Pak and R. Radoiˇci´c, “Hamiltonian paths in Cayley graphs,” Discr. Math., 309, No. 17, 5501-5508 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  11. G. A. Jones, “Automorphism groups of edge-transitive maps,” arXiv:1605.09461 [math.CO].

  12. M. Maˇcaj, “On minimal kaleidoscopic regular maps with trinity symmetry,” The Seventh Workshop Graph Embeddings and Maps on Surfaces, Abstracts, Podbanske, Slovakia (2017).

  13. R. W. Carter, Simple Groups of Lie Type, Pure Appl. Math., 28, Wiley, London (1972).

    Google Scholar 

  14. L. E. Dickson, Linear Groups with an Exposition of the Galois Field Theory, B. G. Teubner, Leipzig (1901).

    MATH  Google Scholar 

  15. D. Gorenstein, Finite Groups, Harper and Row, New York (1968).

  16. Ya. N. Nuzhin, “Generating sets of elements of Chevalley groups over a finite field,” Algebra and Logic, 28, No. 6, 438-449 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  17. V. M. Levchuk, “Remark on a theorem of L. Dickson,” Algebra and Logic, 22, No. 4, 306-316 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  18. Ya. N. Nuzhin, “Groups contained between groups of Lie type over various fields,” Algebra and Logic, 22, No. 5, 378-389 (1983).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660041, Russia

    Ya. N. Nuzhin

Authors
  1. Ya. N. Nuzhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya. N. Nuzhin.

Additional information

Translated from Algebra i Logika, Vol. 58, No. 1, pp. 84-107, January-February, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nuzhin, Y.N. Generating Triples of Involutions of Groups of Lie Type of Rank 2 Over Finite Fields. Algebra Logic 58, 59–76 (2019). https://doi.org/10.1007/s10469-019-09525-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-019-09525-3

Keywords

Search

Navigation