Spanning Subset Sums for Finite Abelian Groups

We survey the state of research to determine the maximum size of a nonspanning subset of a finite abelian group G of order n. The smallest prime factor of n, denote it here by p, plays a crucial role. For prime order, G = Z p , this is essentially an old problem of ErdÅ\u91s and Heilbronn, which can be solved using a result of Dias da Silva and Hamidoune. We provide a simple new proof for the solution when n is even (p = 2). For composite odd n, we deduce the solution, for n 2p 2 , from results obtained years ago by Diderrich and, recently, by Gao and Hamidoune. Only a small family of cases remains unsettled