Remarks on Group Rings and the Davenport Constant

Abstract

Let \(D(G)\) be the Davenport constant of a finite abelian group \(G\), defined as the smallest positive integer \(d\) such that every
sequence of \(d\) elements in \(G\) contains a nonempty subsequence with sum zero the identity of \(G\). In this short note, we use group rings as a tool to characterize the Davenport constant.