Characterization of projective general linear groups

	Characterization of projective general linear groups
International Journal of Group Theory
مقاله 8، دوره 5، شماره 1، خرداد 2016، صفحه 17-28 اصل مقاله (224.78 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2016.5634
نویسنده
Alireza Khalili Asboei^*
Farhangian University, Shariati Mazandaran, Iran
چکیده
‎Let $G$ be a finite group and $\pi_{e}(G)$ be the set of element orders of $G $‎. ‎Let $k \in \pi_{e}(G)$ and $s_{k}$ be the number of elements of order $ ‎k $ in $G$‎. ‎Set nse($G$):=$\{ s_{k} \| k \in \pi_{e}(G)\}$‎. ‎In this paper‎, ‎it‎ ‎is proved if $\|G\|=\|$ PGL$_{2}(q)\|$‎, ‎where $q$ is odd prime power and nse$ ‎(G)= $nse$($PGL$_{2}(q))$‎, ‎then $G \cong $PGL$_{2}(q)$‎.
کلیدواژه‌ها
‎Element order‎؛ ‎set of the numbers of elements of the same order‎؛ ‎projective general linear group

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