Local indicability in ordered groups: Braids and elementary amenable groups
Local indicability in ordered groups: Braids and elementary amenable groups
复制标题
有序组中的局部指示性：辫子和基本顺从组
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
D. Rolfsen
中科院分区：
文献类型：
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作者：
A. Rhemtulla;D. Rolfsen
局部可指示的群也是右序的，但不是相反。本文研究了右序群中局部可标性的一个刻画，其关键概念是Conrad给出的右序群的一个性质。我们的方法回答了一个问题，关于Artin辫子群B n，这是已知的右序。纯辫子的子群P n享有的顺序是不变的乘法下双方，它已被问及是否这样的顺序P n可以扩展到一个右不变的顺序R n。我们的回答是否定的。对Linnell最近的一个结果给出了另一个证明：对于初等顺从群，右序性和局部可导性的概念是一致的。
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. Our methods 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 R n . We answer this in the negative. We also give another proof of a recent result of Linnell that for elementary amenable groups, the concepts of right-orderability and local indicability coincide.