Group theory and generalizations Concept
Left-orderable group
Summary
A left-orderable group is a group with a total order that is preserved by multiplication on the left. Every orderable group is left-orderable, but the converse fails. Braid groups are left-orderable, a result of Dehornoy. Left orders link group theory with dynamics, because countable left-orderable groups are the countable groups that act faithfully on the real line by order-preserving homeomorphisms.
Further reading
About this page
| Tag | F1WYS82NNB |
|---|---|
| URI | m2://F1WYS82NNB |
| Kind | concept |
| Writing | W0 stub |
| MSC | 20F60, 06F15 |
| Specializes | Group |
| Changed | 2 November 2026 |
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