Skip to main content
Log in

Generating sets of elements of Chevalley groups over a finite field

  • Published:
Algebra and Logic Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. N. Bourbaki, Lie Groups and Algebras, IV–VI [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  2. V. M. Levchuk, "Pairs of generating elements," in: Fourth National Symposium on Group Theory [in Russian], Novosibirsk (1973), pp. 117–119.

  3. V. M. Levchuk, "Approximations of free groups by semisimple factors of the groups GL3(q)," in: Questions of Group and Ring Theories [in Russian], Krasnoyarsk (1973), pp. 123–149.

  4. V. M. Levchuk, "Remarks on a theorem of L. Dickson," Algebra Logika,22, No. 4, 504–517 (1983).

    Google Scholar 

  5. V. M. Levchuk, "Generating sets of root elements of Chevalley groups over a field," Algebra Logika,22, No. 5, 526–541 (1983).

    Google Scholar 

  6. V. M. Levchuk and Ya. N. Nuzhin, "Structure of Ree groups," Algebra Logika,24, No. 1, 26–41 (1985).

    Google Scholar 

  7. Ya. N. Nuzhin, "Groups included between Lie type groups over different fields," Algebra Logika,22, No. 5, 526–541 (1983).

    Google Scholar 

  8. Ya. N. Nuzhin, "Structure of Lie groups of rank 1," Mat. Zametki,36, No. 2, 149–158 (1984).

    Google Scholar 

  9. A. A. Albert and J. Thompson, "Two-element generation of the projective unimodular group," Ill. J. Math.,53, No. 3, 421–439 (1959).

    Google Scholar 

  10. R. W. Carter, Simple Groups of Lie Type, Wiley, London (1972).

    Google Scholar 

  11. D. W. Growe, "Generating reflections for U(2, p2n)," Proc. Am. Math. Soc.,13, No. 4, 500–502 (1962).

    Google Scholar 

  12. D. W. Growe, "Generating reflections for U(2, p2n). II, p = 2," Can. Math. Bull.,7, No. 2, 213–217 (1964).

    Google Scholar 

  13. R. Kats and W. Magnus, "Residual properties of free groups," Commun. Pure Appl. Math.,22, No. 1, 1–13 (1969).

    Google Scholar 

  14. A. M. Macbeath, "Generators of the linear fractional groups," in: Proc. Sympos. Pure Math., Vol. 12, Number Theory, Providence, (1969), pp. 14–32.

    Google Scholar 

  15. T. G. Room and R. J. Smith, "A generation of the symplectic group," Quart. J. Math.,9, No. 35, 177–182 (1958).

    Google Scholar 

  16. T. G. Room, "The generation by two operators of the symplectic group over GF(2)," J. Austral. Math. Soc.,1, No. 1, 38–46 (1959).

    Google Scholar 

  17. P. Stanek, Two-element generation of the symplectic group, Bull. Am. Math. Soc.,67, 225–227 (1961).

    Google Scholar 

  18. P. Stanek, "Two element generation of the symplectic group," Trans. Am. Math. Soc.,108, No. 3, 429–436 (1963).

    Google Scholar 

  19. R. Steinberg, "Generators for simple groups," Can. J. Math.,14, No. 2, 277–283 (1962).

    Google Scholar 

Download references

Authors

Additional information

Translated from Algebra i Logika, Vol. 28, No. 6, pp. 670–686, November–December, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nuzhin, Y.N. Generating sets of elements of Chevalley groups over a finite field. Algebra and Logic 28, 438–449 (1989). https://doi.org/10.1007/BF01980235

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01980235

Keywords

Navigation