Characterization of the linear groups PSL (2,11) and PSL (2,13)

We prove the nonsimplicity of a finite group containing an involution $\tau$ such that the quotient group $C(\tau)/{\tau}$ the Frobenius group with an additional factor of odd prime order acting transitively on the nonunit elements of the kernel. Based on this we obtain a characterization of the linear groups PSL (2, 11) and PSL (2, 13).