Two-closure of rank 3 groups in polynomial time

02/08/2022

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by   Saveliy V. Skresanov, et al.

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A finite permutation group G on Ω is called a rank 3 group if it has precisely three orbits in its induced action on Ω×Ω. The largest permutation group on Ω having the same orbits as G on Ω×Ω 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.