Amenable groups with a locally invariant order are locally indicable
Group Theory
2013-04-11 v3
Abstract
We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent subgroup of G, then a left-invariant total order on G can be chosen so that its restriction to H is both left-invariant and right-invariant. Both results follow from recurrence properties of the action of G on its binary relations.
Keywords
Cite
@article{arxiv.1202.4716,
title = {Amenable groups with a locally invariant order are locally indicable},
author = {Peter Linnell and Dave Witte Morris},
journal= {arXiv preprint arXiv:1202.4716},
year = {2013}
}
Comments
10 pages, no figures. Added a proof that the groups with a locally invariant order are the same as the "weakly diffuse" groups of B.Bowditch