19.67 (2018)

Let $G \leqslant \text{Sym}(\Omega)$, where $\Omega$ is finite. The 2-closure $G^{(2)}$ of the group $G$ is defined to be the largest subgroup of $\text{Sym}(\Omega)$ containing $G$ which has the same orbits as $G$ in the induced action on $\Omega \times \Omega$. Is it true that if $G$ is solvable, then every composition factor of $G^{(2)}$ is either a cyclic or an alternating group?