Publications de l'Institut Mathématique, Nouvelle Série Vol. 99(113), pp. 193–201 (2016) 

NSE CHARACTERIZATION OF THE SIMPLE GROUP $L_2(3^n)$Hosein Parvizi Mosaed, Ali Iranmanesh, Abolfazl TehranianDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran; Department of Mathematics, Tarbiat Modares University, Tehran, IranAbstract: Let $G$ be a group and $\pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $\operatorname{nse}(G)$ be the set of the numbers of elements of $G$ of the same order. We prove that the simple group $L_2(3^n)$ is uniquely determined by $\operatorname{nse}(L_2(3^n))$, where $\pi(L_2(3^n))=4$. Keywords: Element order; set of the numbers of elements of the same order; projective special linear group Classification (MSC2000): 20D60; 20D06 Full text of the article: (for faster download, first choose a mirror)
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