Abstract
We address Syskin’s problem on the calculation of the second Euler-Hall function on finite simple groups. The problem is solved for three of the four series of Lie-type groups of rank 1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hall P., “The Eulerian functions of a group,” Quart. J. Math., 7, 134–151 (1936).
The Kourovka Notebook: Unsolved Problems in Group Theory, 15th ed., Sobolev Inst. Math., Novosibirsk (2002).
Erfanian A. and Wiegold J., “A note on growth sequence for finite simple groups,” Bull. Austral. Math. Soc., 51, 495–499 (1995).
Erfanian A. and Rezaei R., “On the growth sequence of PSp(2m, q),” Int. J. Algebra, 1, No. 2, 51–62 (2007).
Erfanian A., “A note on growth sequences of alternating groups,” Arch. Math., 78, No. 4, 257–262 (2002).
Erfanian A., “A note on growth sequences of PSL(m, q),” Southeast Asian Bull. Math., 29, No. 4, 697–713 (2005).
Ushakov Yu. Yu., “Bound of F. Hall’s functions on the Lie type groups of rank 1,” Vladikavkaz. Mat. Zh., 15, No. 2, 50–56 (2012).
Suchkov N. M. and Prikhod’ko D. M., “On the number of generating pairs for the groups L 2(2m) and Sz(22k+1),” Siberian Math. J., 42, No. 5, 975–980 (2001).
Prikhod’ko D. M., “On the number of generating pairs for the prime finite group,” in: Abstracts: V International Conference “Algebra and Number Theory: Contemporary Problems and Applications” [in Russian], TGPU, Tula, 2003, pp. 185–186.
Carter R. W., Simple Groups of Lie Type, John Wiley and Sons, London (1972).
Steinberg R., Lectures on Chevalley Groups, Yale University, New Haven (1968).
Ward H. N., “On Ree’s series of simple groups,” Trans. Amer. Math. Soc., 121, No. 1, 62–89 (1966).
Janko Z. and Thompson J. C., “On a class of finite simple groups of Ree,” J. Algebra, 4, No. 2, 274–292 (1966).
Levchuk V. M. and Nuzhin Ya. N., “Structure of Ree groups,” Algebra and Logic, 24, No. 1, 16–26 (1985).
Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York, Heidelberg, and Berlin (1996).
Levchuk V. M., “F. Hall’s functions on groups of Lie type and groups of rank 1,” Vladikavkaz. Mat. Zh., 10, No. 1, 37–39 (2008).
Hurrelbrink J. and Rehmann U., “Eine endliche Presentation der Gruppe G 2(Z),” Math. Z., Bd 141,Heft 3, 243–251 (1975).
Kemper G., Lübeck F., and Magaard K., “Matrix generators for the Ree groups 2 G 2(q),” Comm. Algebra, 29, No. 1, 407–413 (2001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2013 Levchuk D.V. and Ushakov Yu.Yu.
The authors were supported by the Russian Foundation for Basic Research (Grant 12-01-00968-a).
__________
Translated from Sibirskiı Matematicheskiı Zhurnal, Vol. 54, No. 2, pp. 336–346, March–April, 2013.
Rights and permissions
About this article
Cite this article
Levchuk, D.V., Ushakov, Y.Y. Euler-Hall functions on Ree groups. Sib Math J 54, 256–264 (2013). https://doi.org/10.1134/S0037446613020109
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446613020109