Additive Latin transversals. (Q1567340)

For \(p\) an odd prime the author proves that for any pair of sets \(A,B\subset\mathbb Z/p\mathbb Z\), if \(|A|=|B|\) there exists a bijection \(\phi\:A\to B\) such that the sums \(a+\phi(a)\) are pairwise distinct \((a\in A)\). The author uses the earlier given combinatorial Nullstellensatz [N. Alon, Combin. Probab. Comput. 8, No. 1-2, 7--29 (1999; Zbl 0920.05026)] to prove this. The author thus makes a first step toward a conjecture by Snevily (asserting that one can replace \(\mathbb Z/p\mathbb Z\) with any abelian group having odd order). Finally some extensions are given