On commutativity of circularly ordered c-o-stable groups

A circularly ordered structure is called c-o-stable in $\lambda$, if for any subset $A$ of cardinality at most $\lambda$ and for any cut $s$ there exist at most $\lambda$ one-types over $A$ that are consistent with $s$. A theory is called c-o-stable if there exists an infinite $\lambda$ such that all its models are c-o-stable in $\lambda$. In the paper, it is proved that any circularly ordered group, whose elementary theory is c-o-stable, is Abelian.