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Local indicability in ordered groups: Braids and elementary amenable groups
Author(s):
Akbar
Rhemtulla;
Dale
Rolfsen
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2569-2577.
MSC (2000):
Primary 20F36;
Secondary 20F60, 06F15
Posted:
February 12, 2002
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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  which are known to be right-orderable. The subgroups  of pure braids enjoy an ordering which is invariant under multiplication on both sides, and it has been asked whether such an ordering of  could extend to a right-invariant ordering of  . 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:
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
Posted:
February 12, 2002
Additional Notes:
The authors thank NSERC for partial financial support
Communicated by:
Stephen D. Smith
Copyright of article:
Copyright
2002,
American Mathematical Society
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