Amenable groups with a locally invariant order are locally indicable. (Q399422)
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scientific article; zbMATH DE number 6331648
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Amenable groups with a locally invariant order are locally indicable. |
scientific article; zbMATH DE number 6331648 |
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Amenable groups with a locally invariant order are locally indicable. (English)
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19 August 2014
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Summary: 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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locally invariant orders
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left-invariant orders
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left-orderable groups
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right-orderable groups
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recurrent orders
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locally indicable groups
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amenable groups
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locally nilpotent subgroups
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