Let G be a finite abelian group and p be the smallest prime divisor of |G|. Let S be a sequence over G. We say that S is regular if S contains at most \(|H|-1\) terms from H for every proper subgroup \(H \subsetneq G\) . Let \(\textsf{c}_0(G)\) be the smallest integer t such that every regular sequence S over G of length \(|S|\ge t\) forms an additive basis of G, i.e., \(\sum (S)=G\) . It was conjectured by Gao et al. [2] that \({\textsf{c}}_0(G)=m(G)\) . In this note, we confirm the conjecture for the case when \(G=C_{n_1}\oplus C_{n_2}\) with \(n_1|n_2\) , \(p\ge 11\) and \(n_1\ge p^2\) and we also characterize the structure of regular sequences S over G of length \(|S|={\textsf{c}}_0(G)-1\) with \(\sum (S)\ne G\) .
