Subgroups of Bestvina-Brady groups

2025/02/05 by Simone Blumer, Blumer, Simone
Chemistry · #05C35 #17B56 #20F65 #Combinatorics (math.CO) #Coordination Chemistry and Organometallics #FOS: Mathematics #Group Theory (math.GR) #Organometallic Compounds Synthesis and Characterization #Rings and Algebras (math.RA) #Synthesis and characterization of novel inorganic/organometallic compounds

paper · pdf · doi:10.48550/arxiv.2502.03215

openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In "Subgroups of Graph Groups", 1987, J. Alg., Droms proved that all the subgroups of a right-angled Artin group (RAAG) defined by a finite simplicial graph Γ are themselves RAAGs if, and only if, Γ has no induced square graph nor line-graph of length 3. The present work provides a similar result for specific normal subgroups of RAAGs, called Bestvina-Brady groups: We characterize those graphs in which every subgroup of such a group is itself a RAAG. In turn, we confirm several Galois theoretic conjectures for the pro-p completions of these groups.

Related

• On the structure of finitely presented Bestvina-Brady groups
• Isomorphisms Between Bestsvina--Brady Groups and Right-angled Artin Groups
• Right-angled Artin pro-p groups
• The conjugacy problem in right-angled Artin groups and their subgroups
• Subgroups and quotient groups of automorphism groups of RAAGs