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Finite groups of the same type as Suzuki groups | ||
| International Journal of Group Theory | ||
| مقاله 4، دوره 8، شماره 1، خرداد 2019، صفحه 35-42 اصل مقاله (203.68 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21556 | ||
| نویسندگان | ||
| Seyed Hassan Alavi1؛ Ashraf Daneshkhah* 1؛ Hosein Parvizi Mosaed2 | ||
| 1Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran | ||
| 2Alvand Institute of Higher Education, Hamedan, Iran. | ||
| چکیده | ||
| For a finite group $G$ and a positive integer $n$, let $G(n)$ be the set of all elements in $G$ such that $x^{n}=1$. The groups $G$ and $H$ are said to be of the same (order) type if $|G(n)|=|H(n)|$, for all $n$. The main aim of this paper is to show that if $G$ is a finite group of the same type as Suzuki groups $Sz(q)$, where $q=2^{2m+1}\geq 8$, then $G$ is isomorphic to $Sz(q)$. This addresses to the well-known J. G. Thompson's problem (1987) for simple groups. | ||
| کلیدواژهها | ||
| Suzuki group؛ Thompson's problem؛ Element order | ||
| مراجع | ||
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