Finite Groups with the Same Order and the Same Number of Elements of Maximal Order as the Projective Special Linear Group L 2 q

Abstract

Assume that $G$ is a finite group. It is widely known that $\left|G\right|$ and the number of elements of maximal order in $G$ have something to do with the structure of $G$ . This subject is related to Thompson’s conjecture. In the present paper, we give a complete classification of the groups with the same order and the same number of elements of maximal order as $L_2\left(q\right)$ , where $q=7,17$ .