Two-closure of supersolvable permutation group in polynomial time

12/21/2019

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by   Ilia Ponomarenko, et al.

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The 2-closure G of a permutation group G on Ω is defined to be the largest permutation group on Ω, having the same orbits on Ω×Ω as G. It is proved that if G is supersolvable, then G can be found in polynomial time in |Ω|. As a byproduct of our technique, it is shown that the composition factors of G are cyclic or alternating of prime degree.