Amenable groups with a locally invariant order are locally indicable

2012/02/21 by Peter Linnell, Dave Witte Morris, Linnell, Peter +1 · 1 citation
Mathematics · #06F15 #20F60 #37A05 #43A07 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:06F15 #msc:20F60 #msc:37A05 #msc:43A07

paper · pdf · doi:10.48550/arxiv.1202.4716

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

arxiv created 2013/04/10 · arxiv updated 2013/04/11

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.

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