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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local indicability in ordered groups: Braids and elementary amenable groups


Authors: Akbar Rhemtulla and Dale Rolfsen
Journal: Proc. Amer. Math. Soc. 130 (2002), 2569-2577
MSC (2000): Primary 20F36; Secondary 20F60, 06F15
Published electronically: February 12, 2002
MathSciNet review: 1900863
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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 $B_n$ 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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Additional Information

Akbar Rhemtulla
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: ar@ualberta.ca

Dale Rolfsen
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
Email: rolfsen@math.ubc.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06413-4
PII: S 0002-9939(02)06413-4
Received by editor(s): February 16, 2001
Received by editor(s) in revised form: April 26, 2001
Published electronically: February 12, 2002
Additional Notes: The authors thank NSERC for partial financial support
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society