A characterization of $\mathbf{L_2(81)}$ by nse

Document Type: Research Paper

Authors

1 Department of Mathematical Sciences; Isfahan University of Technology; Isfahan 84156-83111; Iran.

2 Department of Mathematical Sciences;, Isfahan University of Technology

Abstract

Let $\pi_e(G)$ be the set of element orders of a finite group $G$‎. ‎Let $nse(G)=\{m_n\mid n\in\pi_e(G)\}$‎, ‎where $m_n$ be the number of elements of order $n$ in $G$‎. ‎In this paper‎, ‎we prove that if $nse(G)=nse(L_2(81))$‎, ‎then $G\cong L_2(81)$‎.

Keywords

Main Subjects


A‎. ‎K‎. ‎Asboei and S‎. ‎S‎. ‎Salehi Amiri (2012). ‎A new Characterization of $PSL(2,25)$. Int‎. ‎J‎. ‎Group Theory. 1 (3), 15-19
A‎. ‎K‎. ‎Asboei (2014). ‎A new Characterization of $PSL(2,27)$. Bol‎. ‎Soc‎. ‎Paran Math.. , 43-50
J‎. ‎H‎. ‎Conway‎, ‎R‎. ‎Curtis‎, ‎S‎. ‎Norton and R‎. ‎A‎. ‎Wilson (1985). Atlas of Finite Groups. ‎computational assistance from J‎. ‎G‎. ‎Thackray‎, ‎Oxford University Press.
J‎. ‎D‎. ‎Frobenius (1895). Verallgemeinerung des Sylowschen Satse. ‎Berliner Sitz. , 981-993
M‎. ‎Hall (1959). The Theory of Group. ‎The Macmillan Co.‎, ‎New York.
M‎. ‎Herzog (1968). ‎On finite simple groups of order divisible by three primes only. J‎. ‎Algebra. 10, 383-388
B‎. ‎Huppert (1967). Endliche Gruppen I. ‎Grundlehren der Mathematischen Wissenschaften, ‎Springer-Verlag‎, ‎Berlin. 134
M‎. ‎Khatami‎, ‎B‎. ‎Khosravi and Z‎. ‎Akhlaghi‎ (2009). ‎A new characterization for some linear groups. Monatsh‎. ‎Math.. 163, 39-50
C‎. ‎G‎. ‎Shao and Q‎. ‎H‎. ‎Jiang (2014). ‎A new characterization of ${rm PSL}_2(p)$ by NSE. J‎. ‎Algebra Appl.. 13, 24-29
C‎. ‎G‎. ‎Shao‎, ‎W‎. ‎Shi and Q‎. ‎H‎. ‎Jiang (2008). ‎Characterization of simple $K_4$-groups. Front‎. ‎Math‎. ‎China.. 3, 355-370
R‎. ‎Shen‎, ‎C‎. ‎Shao‎, ‎Q‎. ‎Jiang‎, ‎W‎. ‎Shi and V‎. ‎Mazurov (2010). ‎A new characterization of $A_5$. Monatsh‎. ‎Math.. 160, 337-341
W‎. ‎Shi (1991). ‎On simple $K_4$-groups. Chinese Science Bull.. 36, 1281-1283
The GAP Group (2005). ‎GAP‎ - ‎Groups. ‎Algorithms and Programming‎, ‎Version 4.4‎, ‎(href{http://www.gap-system.org}{http://www.gap-system.org}).