# NSE characterization of some linear groups

Document Type : Research Paper

Authors

1 Faculty of Mathematical Sciences‎, ‎Department of Pure Mathematics‎, ‎Shahrekord University‎, ‎Shahrekord‎, ‎Iran.

2 Department of Mathematical Sciences‎, ‎Isfahan University of Technology‎, ‎Isfahan 84156-83111‎, ‎Iran‎.

Abstract

‎For a finite group $G$‎, ‎let $nse(G)=\{m_k\mid k\in\pi_e(G)\}$‎, ‎where $m_k$ is the number of elements of order $k$ in $G$‎ ‎and $\pi_{e}(G)$ is the set of element orders of $G$‎. ‎In this paper‎, ‎we prove that $G\cong L_m(2)$ if and only if $p\mid |G|$ and $nse(G)=nse(L_m(2))$‎, ‎where $m\in \{n,n+1\}$ and $2^n-1=p$ is a prime number.

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Main Subjects

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### History

• Receive Date: 24 April 2016
• Revise Date: 08 October 2016
• Accept Date: 09 October 2016