The \(R_{\infty}\) property for Houghton's groups

The \(R_{\infty}\) property for Houghton's groups

We study twisted conjugacy classes of a family of groups which are called Houghton's groups \(\mathcal{H}_n\) (\(n \in\mathbb{N}\)), the group of translations of \(n\) rays of discrete points at infinity. We prove that the Houghton's groups \(\mathcal{H}_n\) have the \(R_\infty\) property...

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Bibliographic Details
Date:2017
Main Authors: Jo, Jang Hyun, Lee, Jong Bum, Lee, Sang Rae
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2017
Subjects:
Houghton's group
\(R_\infty\) property
Reidemeister number
20E45
20E36
55M20
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/466
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Journal Title:Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics
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Summary:We study twisted conjugacy classes of a family of groups which are called Houghton's groups \(\mathcal{H}_n\) (\(n \in\mathbb{N}\)), the group of translations of \(n\) rays of discrete points at infinity. We prove that the Houghton's groups \(\mathcal{H}_n\) have the \(R_\infty\) property for all \(n\in \mathbb{N}\).

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