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 ${rm nse}(G)={s_m(G) | min pi_e(G)}$. An arbitrary finite group $M$ is NSE characterization if, for every group $G$, the equality ${rm nse}(G)={rm nse}(M)$ implies that $Gcong M$. 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.

Sakineh Rahbariyan

On the NSE characterization of certain finite simple groups

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