Odd-cycle systems with prescribed automorphism groups

It is shown that for any finite group ΓΓ, there exists a (2k+1)(2k+1)-cycle system whose full automorphism group is isomorphic to ΓΓ. Furthermore the minimal order of such a system is at most (4k+1)2γlog2γ(4k+1)2γlog2γ if ΓΓ is non-cyclic, and (4k+1)3γ(4k+1)3γ otherwise, where γ=|Γ|γ=|Γ|.