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

• 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
• Journal Title: Algebra and Discrete Mathematics

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...