Droms Theorems for twisted right-angled Artin groups

TL;DR

This work extends Droms' classical analysis of RAAGs to twisted RAAGs defined by mixed graphs. By introducing Droms mixed graphs and leveraging cone and free-product constructions, it characterizes when all finitely generated subgroups of a T-RAAG are again T-RAAGs, and provides a precise coherence criterion in terms of chordality of the underlying graph. It further develops a rigidity theory for T-RAAGs via the satellite notion, giving a complete criterion for rigidity in the Droms setting and detailing how isomorphisms interact with the defining mixed graphs. The results deepen the understanding of the subgroup structure and isomorphism problem for twisted graph groups, with potential implications for topology and geometric group theory.

Abstract

We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence within this class of groups in terms of the defining graph. Furthermore, we provide a solution to the isomorphism problem for a notable subclass of these groups.

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Theorems & Definitions (50)

• Definition 1
• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Conjecture 1.4
• Definition 2
• Remark 1
• Example 1
• Definition 3
• Remark 2