On 2-closures of rank 3 groups

2020/07/29 by Skresanov, Saveliy V. · 1 citation
#05E18 (Secondary) #20B25 (Primary) 20B15 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2007.14696

Abstract

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 2-closure of a primitive one-dimensional affine rank 3 permutation group of sufficiently large degree is also affine and one-dimensional.

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