The 2-Closure of a 32 -Transitive Group in Polynomial Time Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2019, Volume: 60, Number: 2, Pages: 279-290 Pages count : 12 DOI: 10.1134/S0037446619020083 | ||||
| Tags | 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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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. © 2019, Pleiades Publishing, Ltd.
Cite:
Vasil’ev A.V.
, Churikov D.V.
The 2-Closure of a 32 -Transitive Group in Polynomial Time
Siberian Mathematical Journal. 2019. V.60. N2. P.279-290. DOI: 10.1134/S0037446619020083 WOS Scopus OpenAlex
The 2-Closure of a 32 -Transitive Group in Polynomial Time
Siberian Mathematical Journal. 2019. V.60. N2. P.279-290. DOI: 10.1134/S0037446619020083 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000465640100008 |
| Scopus: | 2-s2.0-85064946503 |
| OpenAlex: | W2941397040 |