Abstract
We demonstrate a number of hard permutation group algorithmic problems, such as Group Intersection and Setwise Stabilizer, which become polynomially equivalent to the Graph Isomorphism Problem after restricting them to 2-closed permutation groups. It is shown that these problems are closely related to problems concerning coherent configurations. We also present a polynomial-time procedure for determining the 2-closure of a nilpotent group. This procedure provides a polynomial-time reduction of the 2-closure problem for odd order groups to the same problem for primitive odd order groups.
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Ponomarenko, I.N. Graph isomorphism problem and 2-closed permutation groups. AAECC 5, 9–22 (1994). https://doi.org/10.1007/BF01196622
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DOI: https://doi.org/10.1007/BF01196622