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Local Indicability in Ordered Groups: Braids and Elementary Amenable Groups

Akbar Rhemtulla and Dale Rolfsen
Proceedings of the American Mathematical Society
Vol. 130, No. 9 (Sep., 2002), pp. 2569-2577
Stable URL: http://www.jstor.org/stable/2699673
Page Count: 9
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Local Indicability in Ordered Groups: Braids and Elementary Amenable Groups
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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 Bn which are known to be right-orderable. The subgroups Pn of pure braids enjoy an ordering which is invariant under multiplication on both sides, and it has been asked whether such an ordering of Pn could extend to a right- invariant ordering of Bn. 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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