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

Jang Hyun Jo, Jong Bum Lee, Sang Rae Lee

Abstract


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 \(n\in \mathbb{N}\).


Keywords


Houghton's group, \(R_\infty\) property, Reidemeister number

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