On the Independence Number of Some Hypergraph

Abstract

For integers 1 =< m < n and a prime p (we require 2 =< m when p = 2), a subset I(p^n; p^m) ={0,...,p^n-1} is described which contains no pm-term cyclic arithmetic progression modulo p^n, and which is maximal among subsets of {0,...,p^n-1} with that property. Furthermore, we investigate the same setting, but for any such group.