# Davenport's constant for groups with large exponent

## TL;DR

This paper establishes new bounds on Davenport's constant for finite abelian groups based on their exponent and order, confirming a conjecture for groups with large exponents.

## Contribution

It proves a conjecture relating Davenport's constant to group parameters, providing bounds depending on the group's exponent relative to its order.

## Key findings

- D(G) xp(G)+|G|/exp(G)-1 for xp(G)|G|
- D(G) sqrt{|G|}-1 for xp(G)<|G|^{1/2}
- Confirmed a conjecture by Balasubramanian and the first author.

## Abstract

Let $G$ be a finite abelian group. We show that its Davenport constant $D(G)$ satisfies $D(G)\leq \exp(G)+\frac{|G|}{\exp(G)}-1$, provided that $\exp(G)\geq\sqrt{|G|}$, and $D(G)\leq 2\sqrt{|G|}-1$, if $\exp(G)<\sqrt{|G|}$. This proves a conjecture by Balasubramanian and the first named author.