On embeddings between outer automorphism groups of right-angled Artin groups

2017/02/15 by Shiro Imamura, Imamura, Shiro
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1702.04809

openalex publication_date 2017/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using abelian coverings of Salvetti complexes, embeddings of outer automorphism groups of right-angled Artin groups (RAAGs) into outer automorphism groups of their particular characteristic subgroups are constructed. Virtual embeddings of outer automorphism groups of finitely generated groups having the unique root property into outer automorphism groups of their particular subgroups are also given. These results provide us with rich examples of (virtual) embeddings between outer automorphism groups of RAAGs. Finite subgroups of pure (outer) automorphism groups of RAAGs are also investigated. p-adic valuations and ℤ_p-ranks of these groups are determined to establish some non-embeddability conditions.

Related

• Subgroups and quotient groups of automorphism groups of RAAGs
• On virtual indicability and property (T) for outer automorphism groups of RAAGs
• Outer space and finiteness properties for symmetric automorphisms of RAAGs, and generalisations
• Right-angled Artin groups and Out(F_n) I: quasi-isometric embeddings
• Subspace arrangements, BNS invariants, and pure symmetric outer\n automorphisms of right-angled Artin groups