Abstract:

In the paper, we prove that if $A$ is an elementary Abelian $TI$-subgroup of order 4 in a group $G$ such that $G=F^*\left(G\right)\cdot A$, and $F^*\left(G\right)$ is a quasi-simple group which covers the group $L_n(q)$ where $q$ is odd, then $F^*\left(G\right)\cong L_2(5).$