Conjugacy in Houghton’s groups. (English) Zbl 1332.20035

Antolín, Y.; Burillo, J.; Martino, A.

Publ. Mat., Barc. 59, No. 1, 3-16 (2015).

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

Keywords:

Houghton groups; infinite permutation groups; conjugacy problem; word problem