Counting and classification of groups with a fixed Davenport constant

Determine, for a fixed positive integer r, how many finite non-abelian groups G satisfy D(G) = r, and develop methods to classify such groups.

Background

The authors highlight that while for a fixed value of the Davenport constant there are finitely many groups, there are no fundamental classification methods in the non-abelian case and even the number of candidates with a given value is unknown.

Their work focuses on small values of the Davenport constant, but they emphasize the broader unresolved need for systematic classification tools and counts for general r.