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Subgroup separability of Artin groups
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-05-07 , DOI: 10.1016/j.jalgebra.2021.04.032
Kisnney Almeida , Igor Lima

We find a condition on the underlying graph of an Artin group that fully determines if it is subgroup separable. As a consequence, an Artin group is subgroup separable if and only if it can be obtained from Artin groups of ranks at most 2 via a finite sequence of free products and direct products with the infinite cyclic group. This result generalizes the Metaftsis-Raptis criterion for Right-Angled Artin groups.



中文翻译:

Artin组的亚组可分离性

我们在Artin组的基础图上找到一个条件,该条件可以完全确定它是否是子组可分离的。结果,当且仅当它可以通过有限的自由产物和具有无限循环基团的直接产物的有限序列从等级为2的Artin组中获得时,Artin组才是可分离的亚组。该结果概括了直角Artin组的Metaftsis-Raptis准则。

更新日期:2021-05-17
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