Local indicability in ordered groups: Braids and elementary amenable groups
A. H. Rhemtulla, Dale Rolfsen · Proceedings of the American Mathematical Society · 2002
Groups which are locally indicable are also right-orderable, but not conversely. This paper considers a characterization of local indicability in right-ordered groups, the key concept being a property of right-ordered groups due to Conrad. Our methods answer a question regarding the Artin braid groups B n B_n which are known to be right-orderable. The subgroups P n P_n of pure braids enjoy an ordering which is invariant under multiplication on both sides, and it has been asked whether such an ordering of P n P_n could extend to a right-invariant ordering of B n B_n . We answer this in the negative. We also give another proof of a recent result of Linnell that for elementary amenable groups, the concepts of right-orderability and local indicability coincide.