University of IsfahanInternational Journal of Group Theory2251-76508120190301Finite groups of the same type as Suzuki groups35422155610.22108/ijgt.2017.21556ENSeyed Hassan AlaviDepartment of Mathematics, Bu-Ali Sina University, Hamedan, IranAshraf DaneshkhahDepartment of Mathematics, Bu-Ali Sina University, Hamedan, IranHosein Parvizi MosaedAlvand Institute of Higher Education, Hamedan, Iran.Journal Article20170308For 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.http://ijgt.ui.ac.ir/article_21556_63d2193bfc7047cda3611ae9155ce682.pdf