A Uniform Proof for the Small Davenport Constant of the Exponent-$p$ Heisenberg Group

Andreas Volkmann

Let $p$ be an odd prime and let $H_{p^3}={\mathrm{UT}}_3({\mathbb{F}}_p)$ be the Heisenberg group of order $p^3$ and exponent $p$. We prove $\mathsf{d}(H_{p^3})=3p-3$. The main i…