Right-angled Artin groups as finite-index subgroups of their outer automorphism groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911794957647872 |
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| author | Wiedmer, Manuel |
| author_facet | Wiedmer, Manuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02033 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Right-angled Artin groups as finite-index subgroups of their outer automorphism groups Wiedmer, Manuel Group Theory 20E36, 20F36 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. |
| title | Right-angled Artin groups as finite-index subgroups of their outer automorphism groups |
| topic | Group Theory 20E36, 20F36 |
| url | https://arxiv.org/abs/2209.02033 |