Precise values of the Davenport constant beyond known cases

Determine the precise value of the large Davenport constant D(G) for finite groups beyond currently settled cases, including abelian groups of rank at least three.

Background

The Davenport constant is a central combinatorial invariant tied to factorization and invariant theory. The authors state that its exact value remains unknown for most finite groups and that even in the abelian case results are largely confined to rank at most two, with further classes only partially resolved.

This underscores a broad unresolved program to compute D(G) across wider families of groups, particularly abelian groups of higher rank and non-abelian groups.

References

Apart from a few cases of finite groups, the precise value of the Davenport constant is unknown. Even in the abelian case, little is known beyond groups of rank at most two.

— A classification of finite groups with small Davenport constant  (2409.00363 - Oh, 2024) in Section 1 (Introduction); Abstract

The proof does not determine the exact Davenport constants of $G_{m,r}$, and it does not show that rank eight is the smallest rank at which eq:conjecture fails.

eq:conjecture:

(G)≤∗(G)+(G)=∗(G)+(G)−1.(G)\le^*(G)+(G) =^*(G)+(G)-1.

— Disproof of a Conjectured Upper Bound for the Davenport Constant  (2609.29878 - Wang, 24 Sep 2026) in Section “Further consequences,” final paragraph