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arXiv · 2611.03290

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 $\Z^d$ 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.

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Lian Duan, Zhenchao Ge, Biao Wang, Chunlin Wang, Boqing Xue. 2026-11-02. On covering systems over finite nilpotent groups and lattices. https://arxiv.org/abs/2611.03290

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