Abelian 1-Factorizations of the Complete Graph

Extending a result by Hartman and Rosa (1985, Europ. J. Combinatorics 6, 45–48), we prove that for any Abelian group G of even order, except forG ≃ Z2nwith n > 2, there exists a one-factorization of the complete graph admitting G as a sharply-vertex-transitive automorphism group.