A finite permutation group $G$ on $\Omega$ is called a rank 3 group if it has precisely three orbits in its induced action on $\Omega \times \Omega$. The largest permutation group on $\Omega$ having the same orbits as $G$ on $\Omega \times \Omega$ is called the 2-closure of $G$. We construct a polynomial-time algorithm which given generators of a rank 3 group computes generators of its 2-closure.
Two-closure of supersolvable permutation group in polynomial time
$\mathbf{2}$-Closure of $\mathbf{\frac{3}{2}}$-transitive group in polynomial time
On 2-closures of rank 3 groups
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