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EXOTIC LEFT-ORDERINGS OF THE FREE GROUPS FROM THE DEHORNOY ORDERING

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  01 April 2011

ADAM CLAY
ADAM CLAY*
Affiliation:
CIRGET, Université du Québec à Montréal, Case postale 8888, Succursale Centre-ville, Montréal QC, Canada H3C 3P8 (email: aclay@cirget.ca)
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Abstract

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We show that the restriction of the Dehornoy ordering to an appropriate free subgroup of the three-strand braid group defines a left-ordering of the free group on k generators, k>1, that has no convex subgroups.

Keywords

left-orderable groupsfree groupsbraid groups

MSC classification

Secondary: 20F36: Braid groups; Artin groups 20E05: Free nonabelian groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 103 - 110
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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