A new result on Davenport constant

Abstract Let G be a finite abelian group of order n and Davenport constant D ( G ) . Let S = 0 h ( S ) ∏ g ∈ G g v g ( S ) ∈ F ( G ) be a sequence with a maximal multiplicity h ( S ) attained by 0 and t = | S | ⩾ n + D ( G ) − 1 . Then 0 ∈ ∑ k ( S ) for every 1 ⩽ k ⩽ t + 1 − D ( G ) . This is a refinement of the fundamental result of Gao [W.D. Gao, A combinatorial problem on finite abelian groups, J. Number Theory 58 (1996) 100–103].