The small Davenport constant of odd-prime Heisenberg groups

Let H(p³) be the exponent-p Heisenberg group of order p³. For every odd prime p, we prove that its small Davenport constant is d(H(p³)) = 3p − 3. The lower bound is given by an explicit product-one-free sequence. For the upper bound, we translate the problem into one about zero-sum blocks in Fₚ². A group-algebra estimate controls subsums in a subgroup fibre, Property B describes the extremal zero-sum-free sequences in Cₚ², and an adjacent-swap argument supplies the required central coordinates.Preprint awaiting external peer review. The accompanying programs provide corroborative finite checks and are not part of the proof. No claim of external verification or recognition is made. The paper and documentation are licensed under CC BY 4.0; the verification programs are licensed under the MIT License.