The validity of a Thompson’s problem for $\rm{PSL(4,7)}$

	The validity of a Thompson’s problem for $\rm{PSL(4,7)}$
AUT Journal of Mathematics and Computing
مقاله 8، دوره 1، شماره 1، اردیبهشت 2020، صفحه 89-94 اصل مقاله (522.26 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2019.16174.1022
نویسندگان
Behrooz Khosravi^* ؛ Cyrus Kalantarpour
Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran
چکیده
Let $\pi_e(G)$ be the set of elements orders of $G$. Also let $s_n$ be the number of elements of order $n$ in $G$ and ${\rm nse}(G)=\{s_n\| n\in\pi_e(G)\}$. In this paper we prove that if $G$ is a group such that ${\rm nse}(G)= {\rm nse}(\rm PSL(4,7))$, $19\big\vert\|G\|$ and $19^2\nmid\|G\|$, then $G\cong{\rm PSL(4,7)}$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $\rm{PSL(4,7)}$.
کلیدواژه‌ها
Thompson’s problem؛ Characterization؛ Number of elements of the same order؛ Projective special linear group؛ Hall subgroup؛ NSE؛ Sporadic groups؛ Python
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