Counterexamples to Two Conjectures in the Kourovka Notebook

V., Skresanov, Saveliy

doi:10.1007/s10469-019-09543-1

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“…It is important to stress that the group G in Theorem 1.2 can have a nonsolvable 2closure; such an example of degree 2 6 has been found in [28].…”

Section: Introductionmentioning

confidence: 99%

On 2-closures of rank 3 groups

2021

Ars Math. Contemp.

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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.

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“…It is important to stress that the group G in Theorem 1.2 can have a nonsolvable 2closure; such an example of degree 2 6 has been found in [28].…”

Section: Introductionmentioning

confidence: 99%