Right-angled Artin groups as finite-index subgroups of their outer automorphism groups
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Date
2022-02-21Type
- Master Thesis
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yes
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Abstract
A right-angled Artin group is a group that admits a finite presentation where the only relations are commutators between two generators. We prove by giving an explicit construction 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 (Z/2Z)^N for some N. For these constructions, we use the group of pure symmetric outer automorphisms, a subgroup of the outer automorphism group of a right-angled Artin group. 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. Show more
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https://doi.org/10.3929/ethz-b-000538688Publication status
publishedPublisher
ETH Zurich, Department of MathematicsSubject
Right-angled Artin groupsOrganisational unit
08802 - Iozzi, Alessandra (Tit.-Prof.)
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ETH Bibliography
yes
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