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.
翻译:以美元计价的限定变换组$G$如果在其对美元/奥米加/时间/美元引起的行动中有精确三个轨道,则称为第3级组$G$。以美元/奥米加/时间/美元计算轨道与美元/奥米加/时间/美元相同的最大变换组$G$G$被称为以美元计价的2倍闭合。我们建造了一种多元时算法,给3级的生成者计算其2倍闭合。