Definition:Ordered Group Automorphism

Definition
Let $\left({G, \circ, \preceq}\right)$ be an ordered group.

An ordered group automorphism from $\left({G, \circ, \preceq}\right)$ to itself is a mapping $\phi: G \to G$ that is both:


 * $(1): \quad$ A group automorphism, that is, a group isomorphism from the group $\left({G, \circ}\right)$ to itself


 * $(2): \quad$ An order isomorphism from the ordered set $\left({G, \preceq}\right)$ to itself.

Also see

 * Definition:Ordered Structure Automorphism