A New Characterization of Projective Special Unitary Groups PSU3(3n)

Open access


One of an important problems in finite groups theory, is characterization of groups by specific property. However, in the way the researchers, proved that some of groups by properties such as, elements order, set of elements with same order, graphs, . . . , are characterizable. One of the other methods, is group characterization by using the order of group and the largest elements order. In this paper, we prove that projective special unitary groups PSU3(3n), where 32n−3n+1 is a prime number, can be uniquely determined by the order of group and the second largest elements order.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] G.Y. Chen About Frobenius groups and 2-Frobenius groups J. Southwest China Normal University 20 (1995) 485–487.

  • [2] G.Y. Chen L.G. He and J.H. Xu A new characterization of Sporadic Simple groups Italian Journal of Pure and Mathematics 30 (2013) 373–392.

  • [3] G.Y. Chen and L.G. He A new characterization of L2(q) where q = pn < 125 Italian Journal of Pure and Mathematics 38 (2011) 125–134.

  • [4] G.Y. Chen and L.G. He A new characterization of simple K4-group with type L2(p) Advanced in Mathematics (China) 43 (2014) 667–670. doi:10.11845/sxjz.165b

  • [5] B. Ebrahimzadeh A. Iranmanesh A. Tehranian and H. Parvizi Mosaed A Characterization of the suzuki groups by order and the Largest elements order Journal of Sciences Islamic Republic of Iran 27 (2016) 353–355.

  • [6] D. Gorenstein Finite Groups (Harper and Row New York 1980).

  • [7] L.G. He and G.Y. Chen A new characterization of L3(q) (q ≤ 8) and U3(q) (q ≤ 11) J. Southwest Univ. (Natur. Sci.) 27 (33) (2011) 81–87.

  • [8] W.M. Kantor and A. Seress Large element orders and the characteristic of Lie-type simple groups J. Algebra 322 (2009) 802–832. doi:10.1016/j.jalgebra.2009.05.004

  • [9] A.S. Kondrat’ev Prime graph components of finite simple groups Mathematics of the USSR-Sbornik 67 (1990) 235–247. doi:10.1070/SM1990v067n01ABEH001363

  • [10] A. Khosravi and B.Khosravi A new characterization of some alternating and symmetric groups (II) Houston J. Math. 30 (2004) 465–478. doi:10.1155/S0161171203202386

  • [11] J. Li W. Shi and D. Yu A characterization of some PGL(2 q) by maximum element orders Bull. Korean Math. Soc. 322 (2009) 802–832. doi:10.4134/BKMS.2015.52.6.2025

  • [12] W.J. Shi A characterization of U3(2n) by their element orders J. Southwest-China Normal Univ. 25 (2000) 353–360. doi:10.13718/j.cnki.xsxb.2000.04.001

  • [13] W.J. Shi Pure quantitative characterization of each finite simples groups J. Progress in Nature Science 4 (1994) 316–326.

  • [14] A.V. Vasilev M.A. Grechkoseerva and V.D. Mazurrov Characterization of finite simple groups bye sepecrum and order J. Algebra and Logic 48 (2009) 385–409. doi:10.1007/s10469-009-9074-9

  • [15] J.S. Williams Prime graph components of finite groups J. Algebra 69 (1981) 487–513. doi:10.1016/0021-8693(81)90218-0

  • [16] A.V. Zavarnitsine Recognition of the simple groups L3(q) by element orders J. Group Theory 7 (2004) 81–97. doi:10.1515/jgth.2003.044

Journal information
Impact Factor

Mathematical Citation Quotient (MCQ) 2018: 0.06

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 174 174 7
PDF Downloads 113 113 4