Skip to content
DraconiticResearch
Search Sources API
186,086 studies31 sourcesUpdated 46 min ago
PreprintarXiv licencearXiv

The small Davenport constant of H27× C3r

  • Andreas Volkmann
Open at sourcePDFDOICite

Abstract

Let H27=UT3(𝔽3) be the nonabelian group of order $27$ and exponent $3$. We prove that d(H27× C3r)=2r+6 for every integer r≥0. The proof combines an affine coefficient identity in the group algebra of an elementary abelian group with a decomposition of the nonorthogonality graph of 𝔽32 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.

Related

  1. The small Davenport constant of E2× C3r for 0≤ r≤3
    Andreas Volkmann
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. A twelve-term exclusion for the small Davenport constant of E2× C3r
    Andreas Volkmann
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. The Davenport constant of low-dimensional boxes
    Benjamin Girard, Alain Plagne
    HALPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsHALarXiv
  4. The Davenport constant of balls and boxes
    Benjamin Girard, Alain Plagne
    HALPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsHAL
  5. The fourth generalized Davenport constant of C53
    Sze Chun Yiu
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{volkmann2026small,
  title = {{The small Davenport constant of $H_27\times C_3^r$}},
  author = {Andreas Volkmann},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19810},
  eprint = {2609.19810},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19810},
}
RIS
TY  - UNPB
TI  - The small Davenport constant of H_27× C_3^r
AU  - Andreas Volkmann
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19810
UR  - https://arxiv.org/abs/2609.19810
AB  - Let H_27=UT_3(𝔽_3) be the nonabelian group of order $27$ and exponent $3$. We prove that d(H_27× C_3^r)=2r+6 for every integer r≥0. The proof combines an affine coefficient identity in the group algebra of an elementary abelian group with a decomposition of the nonorthogonality graph of 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.
ER  -