Geodesic
A new characterization of alternating groups
Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 8-13

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Let $G$ be a finite group and let $\pi_{e}(G)$ be the set of element orders of $G $. Let $k \in \pi_{e}(G)$ and let $m_{k}$ be the number of elements of order $k $ in $G$. Set $\mathrm{nse}(G):=\{ m_{k} | k \in \pi_{e}(G)\}$. In this paper, we show that if $n = r$, $r +1 $, $r + 2$, $r + 3$ $r+4$, or $r + 5$ where $r\geq5$ is the greatest prime not exceeding $n$, then $A_{n}$ characterizable by nse and order.
Keywords: finite group, alternating groups.
Mots-clés : simple group 
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     title = {A new characterization of alternating groups},
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Alireza Khalili Asboei; Syyed Sadegh Salehi Amiri; Ali Iranmanesh. A new characterization of alternating groups. Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 8-13. http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a2/