On 2-closures of rank 3 groups

Saveliy V. Skresanov


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.


2-closure, rank 3 group, rank 3 graph, permutation group

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DOI: https://doi.org/10.26493/1855-3974.2450.1dc

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications