Splitting groups of prime order (Q1092168)

Let M be a finite set of nonzero integers and let G be a finite abelian group. A subset S of G is a splitting set for M if each element in G-\(\{\) \(0\}\) is uniquely expressible in the form ms, \(m\in M\), \(s\in S\) and \(| M| | S| =| G-\{0\}|\). Also M is said to split G. This concept is connected with tiling Euclidean space by translates of certain star bodies. The paper examines splittings primarily in the special case \(M=\{1,2,...,k\}\), where k is a positive integer. In particular in the case where G is a group of prime order the author relates such splittings to Newton sums.