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Groups (possibly semigroups) endowed with possibly left/right/bi-invariant partial/total orderings. Study of such orders on groups.

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Existence of an orbit of exponential growth for group acting on the real line

Let G be a non-abelian finitely generated subgroup of increasing homeomorphisms of the real line having a fixed point free element $h$ ($hx>x$ for all $x$ in the line). Is there a real number $a$ such …
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