论文标题
右角artin群体作为其外构型组的有限索引亚组
Right-angled Artin groups as finite-index subgroups of their outer automorphism groups
论文作者
论文摘要
我们证明，每个右角ARTIN组都是另一个右角Artin组的外部自动形态组的有限索引子组。我们此外表明，可以选择后一个组，以使商对$（\ Mathbb {z}/2 \ Mathbb {z}）^n $的同构为$（\ Mathbb {z}/2 \ Mathbb {z}）^n $。为此，我们使用纯对称外部自动形态的组给出了明确的结构。此外，我们需要在白天和韦德·布鲁克（Wade-Brück）的两个条件，涉及该组何时是一个右角的Artin组以及何时具有有限的索引。
We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is isomorphic to $(\mathbb{Z}/2\mathbb{Z})^N$ for some $N$. For these, we give explicit constructions using the group of pure symmetric outer automorphisms. Moreover, we need two conditions by Day-Wade and Wade-Brück about when this group is a right-angled Artin group and when it has finite index.
