Affiliation:
1. Department of Mathematics , University of Manitoba , Winnipeg , MB R3T 2N2 , Canada
Abstract
Abstract
We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings.
For the case of a left-orderable group, we provide an explicit construction of uncountable families of locally invariant orderings; for a general group, we provide an existence theorem that applies compactness to yield uncountably many locally invariant orderings.
Along the way, we define and investigate the space of locally invariant orderings of a group, the natural group actions on this space, and their relationship to the space of left-orderings.
Funder
Natural Sciences and Engineering Research Council of Canada
Subject
Algebra and Number Theory
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