A note on nilpotent subgroups of automorphism groups of RAAGs

2018/03/22 by Javier Aramayona, Aramayona, Javier, Anthony Genevois +1
Mathematics · #20F18 #20F28 #20F65 #20F67 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1803.08284

openalex publication_date 2018/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We observe that automorphism groups of right-angled Artin groups contain nilpotent non-abelian subgroups, namely H₃(ℤ) the three-dimensional integer Heisenberg group, provided they admit a certain type of element, called an adjacent transvection. This represents a (minor) extension of a result of Charney-Vogtmann.

Related

• Subgroups and quotient groups of automorphism groups of RAAGs
• On solvable subgroups of automorphism groups of right-angled Artin groups
• The R_∞-property for right-angled Artin groups and their nilpotent quotients
• Automorphisms of higher-dimensional right-angled Artin groups
• Finite groups of untwisted outer automorphisms of RAAGs