科研之友
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摘要
Let G be a finite abelian group of order n, and p be the smallest prime dividing n. Let S be a sequence over G. We say that S is regular if for every proper subgroup H subset of G, S contains at most vertical bar H vertical bar - 1 terms from H. Let c(0)(G) be the smallest integer t such that every regular sequence S over G of length vertical bar S vertical bar >= t forms an additive basis of G, i.e. Sigma(S) = G. Recently, c(0)(G) was determined for many abelian groups. In this paper, we determined c(0)(G) for more abelian groups and characterize the structure of the regular sequence S over G of length c(0)(G) - 1 and Sigma(S) not equal G.
