Abstract
We call a partially ordered set Λ sharply transitive if its group of order automorphisms is sharply transitive on Λ, that is, if it is transitive on Λ and every non-trivial automorphism has no fixed points. We show that the direct product of any finite group with an infinite cyclic group is the automorphism group of a sharply transitive partially ordered set. We construct all sharply transitive partially ordered sets whose automorphism group is infinite cyclic. We construct continuously many sharply transitive partially ordered sets whose automorphism group is isomorphic to the additive group of the rational numbers.
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