Literature cited
N. Bourbaki, Lie Groups and Algebras, IV–VI [Russian translation], Mir, Moscow (1975).
V. M. Levchuk, "Pairs of generating elements," in: Fourth National Symposium on Group Theory [in Russian], Novosibirsk (1973), pp. 117–119.
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.
V. M. Levchuk, "Remarks on a theorem of L. Dickson," Algebra Logika,22, No. 4, 504–517 (1983).
V. M. Levchuk, "Generating sets of root elements of Chevalley groups over a field," Algebra Logika,22, No. 5, 526–541 (1983).
V. M. Levchuk and Ya. N. Nuzhin, "Structure of Ree groups," Algebra Logika,24, No. 1, 26–41 (1985).
Ya. N. Nuzhin, "Groups included between Lie type groups over different fields," Algebra Logika,22, No. 5, 526–541 (1983).
Ya. N. Nuzhin, "Structure of Lie groups of rank 1," Mat. Zametki,36, No. 2, 149–158 (1984).
A. A. Albert and J. Thompson, "Two-element generation of the projective unimodular group," Ill. J. Math.,53, No. 3, 421–439 (1959).
R. W. Carter, Simple Groups of Lie Type, Wiley, London (1972).
D. W. Growe, "Generating reflections for U(2, p2n)," Proc. Am. Math. Soc.,13, No. 4, 500–502 (1962).
D. W. Growe, "Generating reflections for U(2, p2n). II, p = 2," Can. Math. Bull.,7, No. 2, 213–217 (1964).
R. Kats and W. Magnus, "Residual properties of free groups," Commun. Pure Appl. Math.,22, No. 1, 1–13 (1969).
A. M. Macbeath, "Generators of the linear fractional groups," in: Proc. Sympos. Pure Math., Vol. 12, Number Theory, Providence, (1969), pp. 14–32.
T. G. Room and R. J. Smith, "A generation of the symplectic group," Quart. J. Math.,9, No. 35, 177–182 (1958).
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).
P. Stanek, Two-element generation of the symplectic group, Bull. Am. Math. Soc.,67, 225–227 (1961).
P. Stanek, "Two element generation of the symplectic group," Trans. Am. Math. Soc.,108, No. 3, 429–436 (1963).
R. Steinberg, "Generators for simple groups," Can. J. Math.,14, No. 2, 277–283 (1962).
Additional information
Translated from Algebra i Logika, Vol. 28, No. 6, pp. 670–686, November–December, 1989.
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01980235