On covering systems over finite nilpotent groups and lattices
Lian Duan, Zhenchao Ge, Biao Wang, Chunlin Wang, Boqing Xue
Abstract
We prove a quantitative non-covering theorem for finite nilpotent groups. As a consequence, every finite covering of 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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