Local indicability in ordered groups: Braids and elementary amenable groups

Rhemtulla, Akbar; Rolfsen, Dale

doi:10.1090/S0002-9939-02-06413-4

Local indicability in ordered groups: Braids and elementary amenable groups
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by Akbar Rhemtulla and Dale Rolfsen PDF

Proc. Amer. Math. Soc. 130 (2002), 2569-2577 Request permission

Abstract:

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 $B_n$ which are known to be right-orderable. The subgroups $P_n$ of pure braids enjoy an ordering which is invariant under multiplication on both sides, and it has been asked whether such an ordering of $P_n$ could extend to a right-invariant ordering of $B_n$. 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.

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