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arXiv · 1202.4716

Amenable groups with a locally invariant order are locally indicable

Peter Linnell·Dave Witte Morris
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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 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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Peter Linnell, Dave Witte Morris. 2012-02-21. Amenable groups with a locally invariant order are locally indicable. https://arxiv.org/abs/1202.4716

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