Abstract
With five exceptions, every finite regular permutation group occurs as the automorphism group of a digraph.
One of the corollaries: given a finite groupG of ordern, there is a commutative semigroupS of order ≤2n+2 such that AutS≅G. The problem whether a latticeL of order ≤Cn with AutL≅G exists (for some constantC), remains open.
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Babai, L. Finite digraphs with given regular automorphism groups. Period Math Hung 11, 257–270 (1980). https://doi.org/10.1007/BF02107568
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DOI: https://doi.org/10.1007/BF02107568