Amenable groups with a locally invariant order are locally indicable | Zendy

Peter A. Linnell | Zendy; Dave Witte Morris | Zendy

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Amenable groups with a locally invariant order are locally indicable

Author(s) -

Peter A. Linnell,

Dave Witte Morris

Publication year - 2014

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/234

Subject(s) - mathematics , invariant (physics) , pure mathematics , amenable group , locally compact space , order (exchange) , locally compact group , algebra over a field , business , mathematical physics , countable set , finance

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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