Definition:Ordered Group Automorphism
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Definition
Let $\struct {G, \circ, \preceq}$ be an ordered group.
An ordered group automorphism from $\struct {G, \circ, \preceq}$ 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 $\struct {G, \circ}$ to itself
- $(2): \quad$ An order isomorphism from the ordered set $\struct {G, \preceq}$ to itself.
Also see
Linguistic Note
The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.
Thus automorphism means self structure.
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