JournalsggdVol. 8, No. 2pp. 467–478

Amenable groups with a locally invariant order are locally indicable

  • Peter Linnell

    Virginia Tech, Blacksburg, USA
  • Dave Witte Morris

    University of Lethbridge, Canada
Amenable groups with a locally invariant order  are locally indicable cover
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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 GG admits a left-invariant total order, and HH is a locally nilpotent subgroup of GG, then a left-invariant total order on GG can be chosen so that its restriction to HH is both left-invariant and right-invariant. Both results follow from recurrence properties of the action of GG on its binary relations.

Cite this article

Peter Linnell, Dave Witte Morris, Amenable groups with a locally invariant order are locally indicable. Groups Geom. Dyn. 8 (2014), no. 2, pp. 467–478

DOI 10.4171/GGD/234