Twisted Conjugacy in Houghton's groups

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For a fixed , the Houghton group consists of bijections of that are ‘eventually translations’ of each copy of . The Houghton groups have been shown to have solvable conjugacy problem. In general, solvable conjugacy problem does not imply that all finite extensions and finite index subgroups have solvable conjugacy problem. Our main theorem is that a stronger result holds: for any and any group G commensurable to , G has solvable conjugacy problem.
Original languageEnglish
Pages (from-to)390-436
Number of pages47
JournalJournal of Algebra
Early online date1 Aug 2017
Publication statusPublished - 15 Nov 2017


  • Uniform twisted conjugacy problem
  • Houghton group
  • Permutation group
  • Orbit decidability
  • Conjugacy problem for commensurable groups
  • Computable centralisers

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