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 .