Snevily's conjecture for cyclic groups

Statement

Let $G$ be an Odd-order cyclic group (?) and $A,B$ be subsets of $G$ of equal size. There exists a bijection $\varphi :A\to B$ such that all the sums $x+\varphi (x),x\in A$, are distinct.

References

Journal references

• Additive Latin transversals by Noga Alon, , Volume 117, Page 125 - 130(Year 2000): ^{PDF copy (Springerlink)More info}
• Tranversals of additive Latin squares by Samit Dasgupta, Gyula Károlyi and Oriol Serra, , Volume 126, Page 17 - 28(Year 2001): ^{PDF copy (Springerlink)More info}