The 2-Closure of a 32 -Transitive Group in Polynomial Time

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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 languageEnglish
Pages (from-to)279-290
Number of pages12
JournalSiberian Mathematical Journal
Volume60
Issue number2
DOIs
Publication statusPublished - 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

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