Sum-free subset of abelian group

Definition
A subset $$S$$ of an Abelian group $$G$$ is termed a sum-free subset if the equation:

$$x + y = z$$

has no solutions for $$x,y,z \in S$$. (Note: We allow $$x,y,z$$ to be possibly equal).

Metaproperties
The property of being a sum-free subset has Freiman rank $$2$$. In other words, if there is a Freiman isomorphism of rank $$2$$ between subsets of Abelian groups, one of them is sum-free if and only if the other one is.

Any subset of a sum-free subset of an Abelian group is again sum-free.