Primitive one-factorizations and the geometry of mixed translations

We construct an infinite family of one-factorizations of K_v admitting an automorphism group acting primitively on the set ofvertices but no such group acting doubly transitively. We also give examples of one-factorizations which are live, in the sense that every one-factor induces an automorphism, but do not coincide with the affine line parallelism of AG(n, 2). To this purpose we develop the notion of a \u201cmixed translation\u201d in AG(n, 2)