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Right-Ordered Groups

Canadian Journal of Mathematics, 1972
A group G is right-ordered if it can be totally ordered so that for any a, b, c in G, a < b implies that ac < bc. Right-ordered groups, considered as order preserving automorphisms of ordered sets, were studied by Cohn in [4]; but the first
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DIAGRAM GROUPS, BRAID GROUPS, AND ORDERABILITY

Journal of Knot Theory and Its Ramifications, 2003
We prove that all diagram groups (in the sense of Guba and Sapir) are left-orderable. The proof is in two steps: firstly, it is proved that all diagram groups inject in a certain braid group on infinitely many strings, and secondly, this group is then shown to be left-orderable.
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