# A Combinatorial Problem on Finite Abelian Groups

```@article{Gao1996ACP,
title={A Combinatorial Problem on Finite Abelian Groups},
author={Weidong Gao},
journal={Journal of Number Theory},
year={1996},
volume={58},
pages={100-103}
}```
• Weidong Gao
• Published 1 May 1996
• Mathematics
• Journal of Number Theory
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 1 , …,  a m in G , 0 can be written in the form 0= a 1 +…+ a i n with 1⩽ i 1 i n ⩽ m , where D ( G ) is the Davenport's constant on G , i.e., the least integer d with the property that for any sequence of d elements in G , there exists a nonempty subsequence that the sum of whose elements is 0.
240 Citations
On n-sum of an abelian group of order n
• Mathematics
• 2013
Let G be an additive finite abelian group of order n, and let S be a sequence of n + k elements in G, where k≥ 1. Assume that S contains t distinct elements. Let P n(S ) denote the set consists of
Weighted sums in finite cyclic groups
• Mathematics
Discret. Math.
• 2004
Product-one subsequences over subgroups of a finite group
• Mathematics
Acta Arithmetica
• 2019
Let G be a finite group, and let D(1)(G) be the smallest integer t such that, every sequence S over G with length |S | ≥ t has a nonempty subsequence T over a cyclic subgroup of G with the product of
On the number of weighted subsequences with zero-sum in a finite abelian group
• Mathematics
• 2015
Suppose G is a finite abelian group and S = g1 ···gl is a sequence of elements in G. For any element g of G and A ⊆ Z\{0}, let NA,g(S) denote the number of subsequences T = Q i∈I gi of S such that P
Note on a Zero-Sum Problem
Let s(G ) be the samllest integer t such that every sequence of t elements in G contains a zero-sum subsequence of length exp(G ), which has been studied by serveral authors during last 20 years.
On zero-sum subsequences in finite Abelian groups.
Let G be a finite abelian group and k ∈ N with k exp(G). Then Ek(G) denotes the smallest integer l ∈ N such that every sequence S ∈ F(G) with |S| ≥ l has a zero-sum subsequence T with k |T |. In this
A Reciprocity on Finite Abelian Groups Involving Zero-Sum Sequences
• Mathematics
SIAM J. Discret. Math.
• 2021
Let G be a finite abelian group. For any positive integers d and m, let φG(d) be the number of elements in G of order d and M(G,m) be the set of all zero-sum sequences of length m. In this paper, for
On zero-sum subsequences of prescribed length
• Mathematics
• 2018
Let G be an additive finite abelian group with exponent exp(G) = m. For any positive integer k, let skm(G) be the smallest positive integer t such that every sequence S in G of length at least t has
Preprint ON WEIGHTED ZERO-SUM SEQUENCES
• Mathematics
• 2010
Let G be a finite additive abelian group with exponent exp(G) = n > 1 and let A be a nonempty subset of {1,. .. , n − 1}. In this paper, we investigate the smallest positive integer m, denoted by