Davenport constant for finite abelian groups with higher rank

For a finite abelian group $G,$ the Davenport Constant, denoted by $D(G)$, is defined to be the least positive integer k such that every sequence of length at least k has a non-trivial zero-sum subsequence. A long-standing conjecture is that the Davenport constant of a finite abelian group G =Cn₁×⋯× Cnd of rank d ∈ N is 1+∑ᵢ₌₁ᵈ (nᵢ-1). This conjecture is false in general, but it remains to know for which groups it is true. In this paper, we consider groups of the form G = (Cₚ)ᵈ⁻¹ × Cpq, where p is a prime and q∈ N and provide sufficient condition when the conjecture holds true.