Document Type : Research Paper

**Authors**

Department of Mathematics, Faculty of Sciences, Arak University, Arak, Iran.

**Abstract**

For a group $G$, $\pi_e(G)$ and $s_m(G)$ are denoted the set of orders of elements and the number of elements of order $m$ in $G$, respectively. Let ${\rm nse}(G)=\{s_m(G) \ | \ m\in \pi_e(G)\}$. An arbitrary finite group $M$ is NSE characterization if, for every group $G$, the equality ${\rm nse}(G)={\rm nse}(M)$ implies that $G\cong M$. In this paper, we are going to show that the non-Abelian finite simple groups $A_9$, $A_{10}$, $A_{12}$, $U_4(3)$, $U_5(2)$, $U_6(2)$, $S_6(2)$, $O_8^+(2)$ and $HS$ are characterizable by NSE.

**Keywords**

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August 2021

Pages 51-65