A statistical approach to covering lemmas

TL;DR

This paper introduces a statistical variant of Ruzsa's covering lemma to analyze the size of subgroups generated by sets with small sumsets in Abelian groups of bounded exponent.

Contribution

It presents a new statistical approach to Ruzsa's covering lemma and derives bounds on subgroup sizes in Abelian groups with small sumsets.

Findings

Subgroups generated by small sumsets are bounded in size by a function of K.

The approach applies to Abelian groups of bounded exponent.

Provides a bound of exp(O(K log^2 K)) times the size of A.

Abstract

We discuss a statistical variant of Ruzsa's covering lemma and use it to show that if G is an Abelian group of bounded exponent and A in G has |A+A| < K|A| then the subgroup generated by A has size at most exp(O(K log^22K))|A|, where the constant in the big-O depends on the exponent of the group only.