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Jahandideh, Maryam, Darafsheh, Mohammad Reza. (1400). Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements. , 11(1), 7-16. doi: 10.22108/ijgt.2021.120906.1594
Maryam Jahandideh; Mohammad Reza Darafsheh. "Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements". , 11, 1, 1400, 7-16. doi: 10.22108/ijgt.2021.120906.1594
Jahandideh, Maryam, Darafsheh, Mohammad Reza. (1400). 'Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements', , 11(1), pp. 7-16. doi: 10.22108/ijgt.2021.120906.1594
Jahandideh, Maryam, Darafsheh, Mohammad Reza. Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements. , 1400; 11(1): 7-16. doi: 10.22108/ijgt.2021.120906.1594

Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements

International Journal of Group Theory
دوره 11، شماره 1، خرداد 2022، صفحه 7-16    اصل مقاله (210.07 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2021.120906.1594
نویسندگان
Maryam Jahandideh* 1؛ Mohammad Reza Darafsheh2
1Department of Mathematics, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran.
2School of Mathematics, Statistics and computer Science, College of Science, University of Tehran, Tehran, Iran.
چکیده
Let $G$ be a group and $\omega(G)=\{o(g)|g\in G\}$ be the set of element orders of $G$. Let $k\in\omega(G)$ and $s_{k}=|\{g\in G|o(g)=k\}|$. Let $nse(G)=\{s_{k}|k\in\omega(G)\}.$ In this paper, we prove that if $G$ is a group and $G_{2}(5)$ is the Chevalley simple group of type $G_{2}$ over $GF(5)$ such that $nse(G)=nse(G_{2}(5))$, then $G\cong G_{2}(5)$.
کلیدواژه‌ها
Element order؛ Thompson's problem؛ Number of the same order elements
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