On additive bases II
Volume 168 / 2015
Acta Arithmetica 168 (2015), 247-267
MSC: 11P70, 11B50, 11B75.
DOI: 10.4064/aa168-3-3
Abstract
Let be an additive finite abelian group, and let S be a sequence over G. We say that S is regular if for every proper subgroup H \subseteq G, S contains at most |H|-1 terms from H. Let \mathsf c_0(G) be the smallest integer t such that every regular sequence S over G of length |S|\geq t forms an additive basis of G, i.e., every element of G can be expressed as the sum over a nonempty subsequence of S. The constant \mathsf c_0(G) has been determined previously only for the elementary abelian groups. In this paper, we determine \mathsf c_0(G) for some groups including the cyclic groups, the groups of even order, the groups of rank at least five, and all the p-groups except G=C_p\oplus C_{p^n} with n\geq 2.
