Coxeter quotients of the automorphism group of a Coxeter group

2020/03/09 by Olga Varghese, Varghese, Olga
Materials Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Supramolecular Self-Assembly in Materials

paper · pdf · doi:10.48550/arxiv.2003.04111

openalex publication_date 2020/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a large class W of Coxeter groups the following holds: Given a group W_Γ in W, the automorphism group \rm Aut(W_Γ) virtually surjects onto some infinite Coxeter group. In particular, the group \rm Aut(W_Γ) is virtually indicable and therefore does not have Kazhdan's property (T).

Related

• Automorphisms of Coxeter groups
• The automorphism group of the universal Coxeter group
• Coxeter groups and automorphisms
• On quotients of Coxeter groups
• Profinite properties of Coxeter groups