# Automorphisms of the totally ordered group Z^n with lexicographical order

It is easy to see that the totally ordered group Z (the integers) with the natural order has no non-trivial automorphisms. Is this also true for Z^n with the lexicographical order?

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I also want to point out that the lexicographic order on $\mathbb{Z}^n$ has no minimal positive element, that is precisely the reason that the argument given by Eric holds. –  Stines Oct 21 '10 at 21:02