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It is shown that a necessary condition for an abstract group G to be the fullautomorphism group of a Hamiltonian cycle system is that G has odd order or itis either binary, or the affine linear group AGL(1; p) with p prime. We showthat this condition is also sufficient except possibly for the class ofnon-solvable binary groups.

On the full automorphism group of a Hamiltonian cycle system of odd order