Local indicability in ordered groups: braids and elementary amenable groups. (English) Zbl 0996.20024
Groups which are locally indicable are also right-orderable, but not conversely. This paper considers a characterization of local indicability in right-ordered groups, the key concept being a property of right-ordered groups due to Conrad. The authors answer a question regarding the Artin braid groups \(B_n\) which are known to be right-orderable. The subgroups \(P_n\) of pure braids enjoy an ordering which is invariant under multiplication on both sides, and it has been asked whether such an ordering of \(P_n\) could extend to a right-invariant ordering of \(B_n\). The authors answer this in the negative. The authors also give another proof of a recent result of Linnell that for elementary amenable groups, the concepts of right-orderability and local indicability coincide.
Reviewer: Meng Jie (Xian)
MSC:
| 20F36 | Braid groups; Artin groups |
| 20F60 | Ordered groups (group-theoretic aspects) |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
| 06F15 | Ordered groups |
Keywords:
local indicability; right-ordered groups; Artin braid groups; pure braids; right-invariant orderings; elementary amenable groupsReferences:
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