TY - JOUR

T1 - The 2-Closure of a 32 -Transitive Group in Polynomial Time

AU - Vasil’ev, A. V.

AU - Churikov, D. V.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

KW - 3/2-homogeneous coherent configuration

KW - 3/2-transitive group

KW - isomorphism of coherent configurations

KW - k-closure of a permutation group

KW - schurian coherent configuration

UR - http://www.scopus.com/inward/record.url?scp=85064946503&partnerID=8YFLogxK

U2 - 10.1134/S0037446619020083

DO - 10.1134/S0037446619020083

M3 - Article

AN - SCOPUS:85064946503

VL - 60

SP - 279

EP - 290

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -