The 2-closure $$\overline{G}$$ G ¯ of a permutation group G on $$\Omega$$ Ω is defined to be the largest permutation group on $$\Omega$$ Ω , having the same orbits on $$\Omega \times \Omega$$ Ω × Ω as G . It is proved that if G is supersolvable, then $$\overline{G}$$ G ¯ can be found in polynomial time in $$|\Omega|$$ | Ω | . As a by-product of our technique, it is shown that the composition factors of $$\overline{G}$$ G ¯ are cyclic or alternating.

中文翻译：

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多项式时间内可解置换群的两个闭包

$$\Omega$$ Ω 上置换群G 的2-闭包$$\overline{G}$$ G¯ 被定义为$$\Omega$$ Ω 上的最大置换群，在$$\Omega \times \Omega$$ Ω × Ω 作为 G 。证明如果G是超可解的，那么$$\overline{G}$$G¯可以在多项式时间内在$$|\Omega|$$|中找到。Ω | . 作为我们技术的副产品，$$\overline{G}$$G¯ 的组成因子是循环的或交替的。