Abstract In this paper the following theorem is proved. Let G be a finite Abelian group of order n . Then, n + D ( G )−1 is the least integer m with the property that for any sequence of m elements a… Expand

Abstract LetGbe a finite abelian group with exponente, letr(G) be the minimal integertwith the property that any sequence oftelements inGcontains ane-term subsequence with sum zero. In this paper we… Expand

Let G be a nite abelian group. The Davenport constant D(G) is the smallest integer ` 2 N such that every sequence S over G of length jSj ` has a nontrivial zero-sum subsequence. Let G = Cn Cn with n… Expand

Summary.Let k ≥ 1 be any integer. Let G be a finite abelian group of exponent n. Let sk(G) be the smallest positive integer t such that every sequence S in G of length at least t has a zero-sum… Expand

It is well known that the maximal possible length of a minimal zero-sum sequence S in the group Z/nZ⊕Z/nZ equals 2n−1, and we investigate the structure of such sequences. We say that some integer n ≥… Expand

Abstract.Let H be an atomic monoid. For $k \in {\Bbb N}$ let ${\cal V}_k (H)$ denote the set of all $m \in {\Bbb N}$ with the following property: There exist atoms (irreducible elements) u1, …, uk,… Expand

The critical number of G, denoted by c(G), is the smallest s such that Σ(S) = G for every subset S of G with cardinality s not containing 0. The parameter c(G) was first studied by Erdős and… Expand