论文标题
染色组中的单词问题和抛物线亚组
Word problem and parabolic subgroups in Dyer groups
论文作者
论文摘要
可以观察到Coxeter组和右角Artin组共享相同的解决方案，以解决问题问题。另一方面，在他对Coxeter组的反思亚组的研究中，Dyer引入了一个群体，我们称之为Dyer群体，其中包含Coxeter组和右角Artin组。我们表明，所有染色组都有解决问题问题的解决方案，我们表明，一个承认该解决方案的组属于我们称之为quasi-dyer群体的一个更一般的组家族，我们表明此包含是严格的。然后，我们显示了准二色组和染料组中的抛物线亚组的几个结果。值得注意的是，我们证明，有限类型的dyer群中抛物线亚组的任何相交是抛物线亚组。
One can observe that Coxeter groups and right-angled Artin groups share the same solution to the word problem. On the other hand, in his study of reflection subgroups of Coxeter groups Dyer introduces a family of groups, which we call Dyer groups, which contains both, Coxeter groups and right-angled Artin groups. We show that all Dyer groups have this solution to the word problem, we show that a group which admits such a solution belongs to a little more general family of groups that we call quasi-Dyer groups, and we show that this inclusion is strict. Then we show several results on parabolic subgroups in quasi-Dyer groups and in Dyer groups. Notably, we prove that any intersection of parabolic subgroups in a Dyer group of finite type is a parabolic subgroup.
