Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order

References

[1] A. K. Asboei, Characterization of projective general linear groups, Int. J. Group Theory 5 (2016), no. 1, 17–28. Search in Google Scholar

[2] A. K. Asboei and S. S. S. Amiri, A new characterization of PSL⁡(2,25), Int. J. Group Theory 1 (2012), no. 3, 15–19. Search in Google Scholar

[3] A. K. Asboei, S. S. S. Amiri, A. Iranmanesh and A. Tehranian, A characterization of symmetric group Sr, where r is prime number, Ann. Math. Inform. 40 (2012), 13–23. Search in Google Scholar

[4] A. K. Asboei, S. S. S. Amiri, A. Iranmanesh and A. Tehranian, A characterization of sporadic simple groups by nse and order, J. Algebra Appl. 12 (2013), no. 2, Article ID 1250158. 10.1142/S0219498812501587Search in Google Scholar

[5] A. K. Asboei, S. S. S. Amiri, A. Iranmanesh and A. Tehranian, A new characterization of A7 and A8, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 21 (2013), no. 3, 43–50. Search in Google Scholar

[6] A. K. Asboei and A. Iranmanesh, A characterization of the linear groups L2⁢(p), Czechoslovak Math. J. 64(139) (2014), no. 2, 459–464. 10.1007/s10587-014-0112-ySearch in Google Scholar

[7] G. Chen, A new characterization of sporadic simple groups, Algebra Colloq. 3 (1996), no. 1, 49–58. Search in Google Scholar

[8] G. Chen, On Thompson’s conjecture, J. Algebra 185 (1996), no. 1, 184–193. 10.1006/jabr.1996.0320Search in Google Scholar

[9] G. Y. Chen, On structure of Frobenius and 2-Frobenius group (in Chinese), J. Southwest China Normal Univ. 20 (1995), no. 5, 485–487. Search in Google Scholar

[10] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Oxford University Press, Eynsham, 1985. Search in Google Scholar

[11] G. Frobenius, Verallgemeinerung des Sylowschen Satzes, Berl. Ber. 1985 (1895), 981–993. Search in Google Scholar

[12] D. Gorenstein, Finite Groups, 2nd ed., Harper and Row, New York, 1980. Search in Google Scholar

[13] B. Huppert, Endliche Gruppen. I, Grundlehren Math. Wiss. 134, Springer, Berlin, 1967. 10.1007/978-3-642-64981-3Search in Google Scholar

[14] N. Iiyori and H. Yamaki, Prime graph components of the simple groups of Lie type over the field of even characteristic, J. Algebra 155 (1993), no. 2, 335–343. 10.1006/jabr.1993.1048Search in Google Scholar

[15] O. H. King, The subgroup structure of finite classical groups in terms of geometric configurations, Surveys in Combinatorics 2005, London Math. Soc. Lecture Note Ser. 327, Cambridge University Press, Cambridge (2005), 29–56. 10.1017/CBO9780511734885.003Search in Google Scholar

[16] A. S. Kondrat’ev, On prime graph components of finite simple groups, Mat. Sb. 180 (1989), no. 6, 787–797, 864. 10.1070/SM1990v067n01ABEH001363Search in Google Scholar

[17] V. D. Mazurov, On infinite groups with abelian centralizers of involution, Algebra Logic 39 (2000), no. 1, 74–86, 121. 10.1007/BF02681567Search in Google Scholar

[18] V. D. Mazurov and E. I. Khukhro, The Kourovka Notebook. Unsolved Problems in Group Theory, Including Archive of Solved Problems, sixteenth ed., Russian Academy of Sciences Siberian Division, Novosibirsk, 2006. Search in Google Scholar

[19] C. Shao, W. Shi and Q. Jiang, Characterization of simple K4-groups, Front. Math. China 3 (2008), no. 3, 355–370. 10.1007/s11464-008-0025-xSearch in Google Scholar

[20] R. Shen, C. Shao, Q. Jiang, W. Shi and V. Mazurov, A new characterization of A5, Monatsh. Math. 160 (2010), no. 3, 337–341. 10.1007/s00605-008-0083-xSearch in Google Scholar

[21] W. J. Shi, A new characterization of the sporadic simple groups, Group Theory (Singapore 1987), De Gruyter, Berlin (1989), 531–540. 10.1515/9783110848397-040Search in Google Scholar

[22] L. Weisner, On the number of elements of a group which have a power in a given conjugate set, Bull. Amer. Math. Soc. 31 (1925), no. 9–10, 492–496. 10.1090/S0002-9904-1925-04087-2Search in Google Scholar

[23] J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), no. 2, 487–513. 10.1016/0021-8693(81)90218-0Search in Google Scholar