Finite groups of the same type as Suzuki groups
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 sam...
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Veröffentlicht in: | International journal of group theory 2019-03, Vol.8 (1), p.35-42 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 2251-7650 2251-7669 |
DOI: | 10.22108/ijgt.2017.21556 |