Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Volkmann, Andreas
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213580017