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Right-angled Artin groups are symmetric diagram groups

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arxiv 2305.11810 v1 pith:YDAGKBNR submitted 2023-05-19 math.GR

Paolo Bellingeri , Anthony Genevois , Neha Nanda This is my paper · ORCID
classification math.GR
keywords groupsdiagramgroupartinright-angledsymmetriceveryarticle
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abstract

In this article, we show that, for every $n \geq 2$, the pure virtual twin group $PVT_n$ can be naturally described as a symmetric diagram group, a family of groups introduced by V. Guba and M. Sapir and associated to semigroup presentations. Inspired by this observation, we prove that every finitely generated right-angled Artin group is a symmetric diagram group. This contrasts with the fact that not all right-angled Artin groups are planar diagram groups.

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Cited by 1 Pith paper

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  1. Combinatorics of affine cactus groups

    math.CO 2025-01 conditional novelty 6.0 of 10

    Affine cactus groups embed into a semidirect product of an affine Gauss diagram group and the symmetric group, yielding linearity, trivial centre, and torsion bounds.

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