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Conjugacy in Houghton’s groups. (English) Zbl 1332.20035
Summary: Let \(n\in\mathbb N\). Houghton’s group \(H_n\) is the group of permutations of \(\{1,\ldots,n\}\times\mathbb N\), that eventually act as a translation in each copy of \(\mathbb N\). We prove the solvability of the conjugacy problem and conjugator search problem for \(H_n\), \(n\geq 2\).

MSC:
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20B07 General theory for infinite permutation groups
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