… Our purpose in this note is to extend the above result to the case of an arbitrary abelian
group, including an infinite one. In order to state the result, we need the following key
concept from [EK1], which we used there to deal with sumset sizes in non-commutative
groups. … We shall now show that all abelian groups have the small sumsets property, a
fact which will be used in Section 3. This will follow easily from the next lemma. …