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arXiv · 2609.19810

The small Davenport constant of $H_{27}\times C_3^r$

Andreas Volkmann
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Abstract

Let $H_{27}=\mathrm{UT}_3(\mathbb{F}_3)$ be the nonabelian group of order $27$ and exponent $3$. We prove that $\mathsf{d}(H_{27}\times C_3^r)=2r+6$ for every integer $r\geq0$. The proof combines an affine coefficient identity in the group algebra of an elementary abelian group with a decomposition of the nonorthogonality graph of $\mathbb{F}_3^2$ into eight edge-disjoint zero-sum triangles. It is uniform in $r$, does not use the value of the small Davenport constant for a smaller nonabelian group, and requires no computational enumeration.

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Andreas Volkmann. 2026-09-17. The small Davenport constant of $H_{27}\times C_3^r$. https://arxiv.org/abs/2609.19810

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