Definition:Ordered Subgroup

Definition
An ordered subgroup $\left({T, \circ, \preceq}\right)$ of an ordered structure $\left({S, \circ, \preceq}\right)$ is an ordered group such that the group $\left({T, \circ}\right)$ is a subgroup of $\left({S, \circ}\right)$.

Also see

 * Ordered Structure