The $3$-closure of a solvable permutation group is solvable

E. A. O'Brien, I. Ponomarenko, A. V. Vasil'ev +1

Let $m$ be a positive integer and let $\Omega$ be a finite set. The $m$-closure of $G\le \mathrm{Sym}(\Omega )$ is the largest permutation group on $\Omega$ having the same orbits as $G$ in…