BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks

Khalili Asboei A. Characterization of $mathrm{PSL}(5,q)$ by its Order and One Conjugacy Class Size. IJMSI. 2020; 15 (1) :35-40

URL: http://ijmsi.ir/article-1-1061-en.html

URL: http://ijmsi.ir/article-1-1061-en.html

Let $p=(q^4+q^3+q^2+q+1)/(5,q-1)$ be a prime number, where $q$ is a prime

power. In this paper, we will show $Gcong mathrm{PSL}(5,q)$ if and only if

$|G|=|mathrm{PSL}(5,q)|$, and $G$ has a conjugacy class size $frac{|

mathrm{PSL}(5,q)|}{p}$. Further, the validity of a conjecture of J. G.

Thompson is generalized to the groups under consideration by a new way.

Type of Study: Research paper |
Subject:
Special

1. N. Ahanjideh, On Thompson's conjecture for some nite simple groups, J. Algebra, 344,(2011), 205-228. [DOI:10.1016/j.jalgebra.2011.05.043]

2. S. S. Amiri, A. K. Asboei, Characterization of some nite groups by order and length of one conjugacy class, Sib. Math. J, 57(2), (2016), 185-189. [DOI:10.1134/S0037446616020014]

3. A. K. Asboei, New characterization of symmetric groups of prime degree, Acta Univ.Sapientiae Math, 9(1), (2017), 5-12. [DOI:10.1515/ausm-2017-0001]

4. A. K. Asboei, A new characterization of PSL(3; q), Jordan J. Math. Stat, 10(4), (2017),307-317.

5. A. K. Asboei, R. Mohammadyari, M. Rahimi, New characterization of some linear groups,Int. J. Industrial Mathematics, 8(2), (2016), 165-170.

6. A. K. Asboei, R. Mohammadyari, Recognizing alternating groups by their order and one conjugacy class length, J. Algebra. Appl, 15(2), (2016), 1650021. [DOI:10.1142/S0219498816500213]

7. A. K. Asboei, R. Mohammadyari, Characterization of the alternating groups by their order and one conjugacy class length, Czechoslovak Math. J, 66(141), (2016), 63-70. [DOI:10.1007/s10587-016-0239-0]

8. A. K. Asboei, R. Mohammadyari, M. R. Darafsheh, The in uence of order and conjugacy class length on the structure of nite groups, Hokkaido Math. J, 47, (2018), 25-32. [DOI:10.14492/hokmj/1520928059]

9. G. Y. Chen, On Frobenius and 2-Frobenius group, J. Southwest China Normal Univ, 20, (1995), 485-487. (in Chinese).

10. G. Y. Chen, On Thompson's conjecture, J. Algebra, 185(1), (1996), 184-193. [DOI:10.1006/jabr.1996.0320]

11. G. Y. Chen, Further rections on Thompson's conjecture, J. Algebra, 218, (1999),276-285. [DOI:10.1006/jabr.1998.7839]

12. G. Y. Chen, A new characterization of sporadic simple groups, Algebra Colloq, 3(1),(1996), 49-58.

13. Y. Chen, G. Y. Chen, Recognizing PSL(2; p) by its order and one special conjugacy class size, J. Inequal. Appl, (2012), 310. [DOI:10.1186/1029-242X-2012-310]

14. Y. H. Chen, G. Y. Chen, Recognization of Alt10 and PSL(4; 4) by two special conjugacy class size, Ital. J. Pure Appl. Math, 29, (2012), 387-394.

15. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Wilson, Atlas of nite groups, Clarendon, Oxford, 1985.

16. M. Foroudi ghasemabadi, N. Ahanjideh, Characterization of the simple groups Dn(3) by prime graph and spectrum, Iran. J. Math. Sci. Inform, 7(1), (2012), 91-106.

17. A. Iranmanesh, S. H. Alavi, A characterization of simple group PSL(5; q), Bull. Austral. Math. Soc, 65, (2002), 211-222. [DOI:10.1017/S0004972700020256]

18. N. Iiyori, H. Yamaki, Prime graph components of the simple groups of Lie type over the eld of even characteristic, J. Algebra, 155(2), (1993), 335-343. [DOI:10.1006/jabr.1993.1048]

19. E. I. Khukhro, V. D. Mazurov, Unsolved Problems in Group Theory, The Kourovka Notebook, 17th edition, Sobolev Institute of Mathematics, Novosibirsk, 2010.

20. A. S. Kondtratev, V. D. Mazurov, Recognition of Alternating groups of prime degree from their element orders, Sib. Math. J, 41(2), (2000), 294-302. [DOI:10.1007/BF02674599]

21. J. B. Li, Finite groups with special conjugacy class sizes or generalized permutable subgroups, (2012), (Chongqing: Southwest University).

22. G. R. Rezaeezadeh, M. R. Darafsheh, M. Bibak, M. Sajjadi, OD-characterization of Almost Simple Groups Related to D4(4), Iran. J. Math. Sci. Inform, 10(1), (2015), 23-43.

23. J. S. Williams, Prime graph components of nite groups, J. Algebra, 69(2), (1981),487-513. [DOI:10.1016/0021-8693(81)90218-0]