# On primitive $2$-closed permutation groups of rank at most four

@inproceedings{Giudici2021OnP, title={On primitive \$2\$-closed permutation groups of rank at most four}, author={Michael Giudici and Luke Morgan and Jin-Xin Zhou}, year={2021} }

We characterise the primitive 2-closed groups G of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or G 6 AΓL1(p ), the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.

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