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Dyer groups: Centres, hyperbolicity, and acylindrical hyperbolicity

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arxiv 2410.22464 v1 pith:7HAXA2I3 submitted 2024-10-29 math.GR

Mireille Soergel , Nicolas Vaskou This is my paper · ORCID
classification math.GR
keywords dyercentresgammagroupshyperbolichyperbolicityacylindricalacylindricality
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abstract

In this article we describe the centres of all Dyer groups. We also give a complete classification of when a Dyer group $D(\Gamma)$ is hyperbolic or acylindricality hyperbolic, with conditions that can easily be read on the Dyer graph $\Gamma$.

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  1. Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups

    math.GR 2025-04 conditional novelty 7.0 of 10

    Periagroups that are infinite and not virtually direct products contain contracting elements in their standard Cayley graphs, implying acylindrical hyperbolicity and transcendental conjugacy growth series.

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