A new characterization of $L_2(q)$ by the largest element orders

Document Type : Research Paper


1 School of Mathematical Sciences‎, ‎University of Jinan‎, ‎250022‎, ‎Shandong‎, ‎China.

2 Department of Mathematics‎, ‎Chongqing University of Arts and Sciences‎, ‎402106‎, ‎Chongqing‎, ‎China.

3 School of Science‎, ‎NanTong University‎, ‎226019‎, ‎Jiangsu‎, ‎China.


‎We characterize the finite simple groups $L_2(q)$ by the group orders and the largest‎ ‎element orders‎, ‎where $q$ is a prime or $q=2^a$‎, ‎with $2^a+1$ or $2^a-1$ a prime‎.


Main Subjects

R. Brauer and W.F. Reynolds, On a problem of E. Artin, Ann. of Math. (2)68 (1958) 713--720.
G.Y. Chen, On structure of Frobenius groups and 2-Frobenius groups (in Chinese), J. Southwest China Norm. Univ. (Nat. Sci.)20 (1995), no. 5, 185--187.
J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson, Atlas of Finite Groups, Oxford Univ. Press, London, 1985.
M.R. Darafsheh, N.S. Karamzadeh and A.R. Moghaddamfar, Relation between Frobenius and 2-Frobenius groups with order components of nite groups, J. Appl. Math. Computing 21 (2006), no. 1-2, 437--450.
The GAP Group, GAP -- Groups, Algorithms, and Programming, Version 4.4.12, 2008.
L.G. He and G.Y. Chen, A new characterization of L2(q) where pn < 125, Ital. J. Pure Appl. Math. 28 (2011) 127--136.
L.G. He and G.Y. Chen, A new characterization of simple K3-groups, Comm. Algebra 40 (2012), no. 10, 3903--3911.
B. Huppert, Endliche Gruppen I, Grundlehren. Math. Wiss. 134, Springer Verlag, Berlin, Heidelberg, New York, 1967.
N.Yu. Makarenko, E.I. Khukhro and P. Shumyatsky, Fixed points of frobenius groups of automorphisms, Dokl. Math. 83 (2011), no. 2, 152--154, .
A.V. Vasilev, M.A. Grechkoseeva and V.D. Mazurov, Characterization of finite simple groups by spectrum and order, Algebra Logic 48 (2009), no. 6, 385--409.
J.S. William, Prime graph components of finite simple groups, J. Algebra69 (1981), no. 1, 487--573.
Q.L. Zhang and W.J. Shi, A new characterization of simple K3-groups and some L2(p), Algebra Colloq. 20 (2013), no. 3, 361--368. 
Volume 43, Issue 5
October 2017
Pages 1143-1151
  • Receive Date: 25 August 2013
  • Revise Date: 08 May 2016
  • Accept Date: 09 May 2016
  • First Publish Date: 31 October 2017