Odd-cycle systems with prescribed automorphism groups

It is shown that for any finite group Γ , there exists a ( 2 k + 1 ) -cycle system whose full automorphism group is isomorphic to Γ . Furthermore the minimal order of such a system is at most ( 4 k + 1 ) 2 γ log 2 γ if Γ is non-cyclic, and ( 4 k + 1 ) 3 γ otherwise, where γ = | Γ | .