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I show that a group of order-automorphisms of a linearly ordered set can be expressed as an unrestricted direct product in which each factor is either the infinite cyclic group or else a group of order-automorphisms of a densely ordered set. From this a couple of simple group embedding theorems can be derived. The technique used to obtain the main result of this paper was motivated by the Erdos-Hajnal inductive classification of scattered sets. Unless the contrary is either obvious or stateddoi:10.1017/s000497270003673x fatcat:z32frux5hrbqdhpahl7ic53fty