Unperforated partially ordered group

Definition
A partially ordered group $$G$$ (with $$G^+$$ denoting the positive cone of $$G$$) is termed unperforated if, for any $$g \in G$$ and any positive integer $$n$$, $$g^n \in G^+ \implies g \in G^+$$. Intuitively, it means there are no gaps (perforations) in the positive cone of $$G$$.