Geodesic
Amenable groups with a locally invariant order are locally indicable
Peter Linnell1 ; Dave Witte Morris2
1Virginia Tech, Blacksburg, USA
2University of Lethbridge, Canada
Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 467-478

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DOI

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.
DOI : 10.4171/ggd/234
Classification : 20-XX
Mots-clés : Locally invariant order, left-invariant order, left-orderable group, right-orderable group, recurrent order, locally indicable, amenable group

Peter Linnell  1   ; Dave Witte Morris  2

1 Virginia Tech, Blacksburg, USA
2 University of Lethbridge, Canada 
Peter Linnell; Dave Witte Morris. Amenable groups with a locally invariant order  are locally indicable. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 467-478. doi: 10.4171/ggd/234
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     title = {Amenable groups with a locally invariant order  are locally indicable},
     journal = {Groups, geometry, and dynamics},
     pages = {467--478},
     year = {2014},
     volume = {8},
     number = {2},
     doi = {10.4171/ggd/234},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/234/}
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