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Conjugacy in Houghton's groups

Y. Antolín, J. Burillo, and A. Martino

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Let $n\in {\mathbb N}$. Houghton's group $H_n$ is the group of permutations of $\{1,\dotsc, n\}\times {\mathbb N}$, 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 $H_n$, $n\geq 2$.

Article information

Publ. Mat., Volume 59, Number 1 (2015), 3-16.

First available in Project Euclid: 21 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 20B99: None of the above, but in this section

Houghton group permutation groups conjugacy problem


Antolín, Y.; Burillo, J.; Martino, A. Conjugacy in Houghton's groups. Publ. Mat. 59 (2015), no. 1, 3--16.

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