Let G 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 ⊆ G, S contains at most |H|-1 terms from H. Let ₀(G) be the smallest integer t such that every regular sequence S over G of length |S| ≥ 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 ₀(G) has been determined previously only for the elementary abelian groups. In this paper, we determine 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 with n≥ 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-3-3,
author = {Weidong Gao and Dongchun Han and Guoyou Qian and Yongke Qu and Hanbin Zhang},
title = {On additive bases II},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {247-267},
zbl = {1330.11064},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-3-3}
}
Weidong Gao; Dongchun Han; Guoyou Qian; Yongke Qu; Hanbin Zhang. On additive bases II. Acta Arithmetica, Tome 168 (2015) pp. 247-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-3-3/