## Abstract

Let G be a permutation group on a finite set Ω. The k-closure G
^{(k)}
of G is the largest subgroup of the symmetric group Sym(Ω) having the same orbits with G on the kth Cartesian power Ω
^{k}
of Ω. The group G is called 32-transitive, if G is transitive and the orbits of a point stabilizer G
_{α}
on Ω{α} are of the same size greater than 1. We prove that the 2-closure G
^{(2)}
of a 32-transitive permutation group G can be found in polynomial time in size of Ω. Moreover, if the group G is not 2-transitive, then for every positive integer k its k-closure can be found within the same time. Applying the result, we prove the existence of a polynomial-time algorithm for solving the isomorphism problem for schurian 32-homogeneous coherent configurations, that is coherent configurations naturally associated with 32-transitive groups.

Original language | English |
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Pages (from-to) | 279-290 |

Number of pages | 12 |

Journal | Siberian Mathematical Journal |

Volume | 60 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Mar 2019 |

## Keywords

- 3/2-homogeneous coherent configuration
- 3/2-transitive group
- isomorphism of coherent configurations
- k-closure of a permutation group
- schurian coherent configuration