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Mathematics > Group Theory

arXiv:2212.07111 (math)
[Submitted on 14 Dec 2022 (v1), last revised 25 Jul 2023 (this version, v2)]

Title:Conjugacy languages in virtual graph products

Authors:Gemma Crowe
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Abstract:In this paper we study the behaviour of conjugacy languages in virtual graph products, extending results by Ciobanu, Hermiller, Holt and Rees. We focus primarily on virtual graph products in the form of a semi-direct product. First, we study the behaviour of twisted conjugacy representatives in right-angled Artin and Coxeter groups. We prove regularity of the conjugacy geodesic language for virtual graph products in certain cases, and highlight properties of the spherical conjugacy language, depending on the automorphism and ordering on the generating set. Finally, we give a criterion for when the spherical conjugacy language is not unambiguous context-free for virtual graph products. We can extend this further in the case of virtual RAAGs, to show the spherical conjugacy language is not context-free.
Comments: Updated with referee corrections, accepted to Journal of Algebra
Subjects: Group Theory (math.GR)
MSC classes: 20F10, 20E45, 20F65, 68Q45
Cite as: arXiv:2212.07111 [math.GR]
  (or arXiv:2212.07111v2 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.2212.07111
Related DOI: https://doi.org/10.1016/j.jalgebra.2023.06.029

Submission history

From: Gemma Crowe [view email]
[v1] Wed, 14 Dec 2022 09:04:41 UTC (53 KB)
[v2] Tue, 25 Jul 2023 19:07:56 UTC (56 KB)
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