The Davenport constant of a finite Abelian group is defined to be the length of the longest minimal zero-system of and is denoted . Symbolically,

for completeness.

In order words, if is a finite Abelian group of order , then the Davenport constant of is the minimal such that every sequence of elements of with length contains a nonempty subsequence with a zero-sum.

Some values of the Davenport constant include the following.

1. .

2. Let be a finite -group. Then .

3. Let with . Then

One open question in finite group theory is the determination of a general formula for .