The Davenport constant of the group \(C_2^{r-1} \oplus C_{2k}\) (Q2692190)

Summary: Let \(G\) be a finite abelian group. The Davenport constant \(\mathsf{D}(G)\) is the maximal length of minimal zero-sum sequences over \(G\). For groups of the form \(C_2^{r-1} \oplus C_{2k}\) the Davenport constant is known for \(r\leqslant 5\). In this paper, we get the precise value of \(\mathsf{D}(C_2^5 \oplus C_{2k})\) for \(k\geqslant 149\). It is also worth pointing out that our result can imply the precise value of \(\mathsf{D}(C_2^4 \oplus C_{2k})\).