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On covering systems over finite nilpotent groups and lattices

  • Lian Duan
  • Zhenchao Ge
  • Biao Wang
  • Chunlin Wang
  • Boqing Xue
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Abstract

We prove a quantitative non-covering theorem for finite nilpotent groups. As a consequence, every finite covering of Zd by affine full-rank sublattices with pairwise distinct indices contains a member of bounded index, uniformly in d. We also establish a summability criterion allowing repeated indices, which extends to finite groups containing a normal nilpotent subgroup of bounded index.

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Cite

BibTeXRIS
BibTeX
@misc{duan2026covering,
  title = {{On covering systems over finite nilpotent groups and lattices}},
  author = {Lian Duan and Zhenchao Ge and Biao Wang and Chunlin Wang and Boqing Xue},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03290},
  eprint = {2611.03290},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03290},
}
RIS
TY  - UNPB
TI  - On covering systems over finite nilpotent groups and lattices
AU  - Lian Duan
AU  - Zhenchao Ge
AU  - Biao Wang
AU  - Chunlin Wang
AU  - Boqing Xue
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03290
UR  - https://arxiv.org/abs/2611.03290
AB  - We prove a quantitative non-covering theorem for finite nilpotent groups. As a consequence, every finite covering of Z^d by affine full-rank sublattices with pairwise distinct indices contains a member of bounded index, uniformly in d. We also establish a summability criterion allowing repeated indices, which extends to finite groups containing a normal nilpotent subgroup of bounded index.
ER  -