%0 Journal Article
%T Finite groups of the same type as Suzuki groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Alavi, Seyed Hassan
%A Daneshkhah, Ashraf
%A Parvizi Mosaed, Hosein
%D 2019
%\ 03/01/2019
%V 8
%N 1
%P 35-42
%! Finite groups of the same type as Suzuki groups
%K Suzuki group
%K Thompson's problem
%K Element order
%R 10.22108/ijgt.2017.21556
%X 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.
%U https://ijgt.ui.ac.ir/article_21556_63d2193bfc7047cda3611ae9155ce682.pdf