TY - JOUR

T1 - On 2-closures of rank 3 groups

AU - Skresanov, Saveliy V.

N1 - Funding Information: *The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. E-mail address: skresan@math.nsc.ru (Saveliy V. Skresanov) Publisher Copyright: © 2021 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.

PY - 2021

Y1 - 2021

N2 - A permutation group G on Ω is called a rank 3 group if it has precisely three orbits in its induced action on Ω×Ω. The largest permutation group on Ω having the same orbits as G on Ω× Ω is called the 2-closure of G. A description of 2-closures of rank 3 groups is given. As a special case, it is proved that the 2-closure of a primitive one-dimensional affine rank 3 group of sufficiently large degree is also affine and one-dimensional.

AB - A permutation group G on Ω is called a rank 3 group if it has precisely three orbits in its induced action on Ω×Ω. The largest permutation group on Ω having the same orbits as G on Ω× Ω is called the 2-closure of G. A description of 2-closures of rank 3 groups is given. As a special case, it is proved that the 2-closure of a primitive one-dimensional affine rank 3 group of sufficiently large degree is also affine and one-dimensional.

KW - 2-closure

KW - Permutation group

KW - Rank 3 graph

KW - Rank 3 group

UR - http://www.scopus.com/inward/record.url?scp=85118172717&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.2450.1dc

DO - 10.26493/1855-3974.2450.1dc

M3 - Article

AN - SCOPUS:85118172717

VL - 21

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

IS - 1

M1 - #P1.08

ER -