O-stable ordered groups

An ordered structure $\mathcal M$ is said to be o-$\lambda$-stable if, for every $A\subseteq\mathcal M$ with $|A|\le\lambda$ and every cut in $\mathcal M$, at most $\lambda$ 1-types over $A$ are consistent with the cut. In the present article, we prove that every o-stable group is abelian. We also study definable subsets and unary functions of o-stable groups.