The Brown–Erdős–Sós conjecture in finite abelian groups

Abstract

The Brown–Erdős–Sós conjecture, one of the central conjectures in extremal combinatorics, states that for any integer m≥6, if a 3-uniform hypergraph on n vertices contains no m vertices spanning at least m−3 edges, then the number of edges is o(n2). We prove the conjecture for triple systems coming from finite abelian groups.