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The lexicographic power ∆ Γ of chains ∆ and Γ is, roughly, the Cartesian power γ∈Γ ∆, totally ordered lexicographically from the left. Here the focus is on certain powers in which either ∆ = R or Γ = R, with emphasis on when two such powers are isomorphic and on when ∆ Γ is 2-homogeneous. The main results are:

We study, from a constructive computational point of view, the techniques used to solve the conjugacy problem in the " generic " lattice-ordered group Aut(R). We use these techniques in order to show that for all f, g ∈ Aut(R), the equation xf x = g is effectively solvable in Aut(R).

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