Irredundant hyperplane covers

János Nagy, Péter Pál Pach, István Tomon

We prove that if $G$ is an abelian group and $H_1{x}_1,\dots ,H_k{x}_k$ is an irredundant (minimal) cover of $G$ with cosets, then $$|G:\bigcap _{i=1}^k{H}_i|=2^{O(k)}.$$ This bound…