Geodesic
NSE Characterization of the Simple Group $L_2(3^n)$
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 193 .

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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 $|\pi(L_2(3^n))|=4$.
DOI : 10.2298/PIM141220015M
Classification : 20D60 20D06
Keywords: Element order, set of the numbers of elements of the same order, projective special linear group 
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     title = {NSE {Characterization} of the {Simple} {Group} $L_2(3^n)$},
     journal = {Publications de l'Institut Math\'ematique},
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Hosein Parvizi Mosaed; Ali Iranmanesh; Abolfazl Tehranian. NSE Characterization of the Simple Group $L_2(3^n)$. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 193 . doi : 10.2298/PIM141220015M. http://geodesic.mathdoc.fr/articles/10.2298/PIM141220015M/

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