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arXiv · 2502.03215

Subgroups of Bestvina-Brady groups

Simone Blumer
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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 $\Gamma$ are themselves RAAGs if, and only if, $\Gamma$ 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.

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Simone Blumer. 2025-02-05. Subgroups of Bestvina-Brady groups. https://arxiv.org/abs/2502.03215

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