On the structure of finite groups with the given numbers of involutions

Let $G$ be a finite non-solvable group. In this paper, we show that if $1/8$ of elements of $G$ have order two, then $G$ is either a simple group isomorphic to $PSL_{2}insert ignore into journalissuearticles values(q);$, where $q\in\{7,8,9\}$ or $G\cong GL_{2}insert ignore into journalissuearticles values(4);.\mathbb{Z}_2 In fact in this paper, we answer Problem 132 in [1].