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

Результат исследования: Научные публикации в периодических изданияхстатья

1 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)279-290
Число страниц12
ЖурналSiberian Mathematical Journal
Том60
Номер выпуска2
DOI
СостояниеОпубликовано - 1 мар 2019

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