Dehn's problems and Houghton's groups

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• Charles Cox Southampton University
• Friday 31 October 2014, 15:00-16:00
• CMS, MR4.

If you have a question about this talk, please contact Julian Brough.

Deciding whether or not two elements of a group are conjugate might seem like a trivial problem. However, there exist finitely presented groups where this question is undecidable: there is no algorithm to output yes or no for any two elements chosen. In this talk Houghton groups (a family of groups all having solvable conjugacy problem) will be introduced as will the idea of twisted conjugacy: a generalisation of the conjugacy problem where an automorphism is also given. This will be our main tool in answering whether finite extensions and finite index subgroups of any Houghton group have solvable conjugacy problem.

This talk is part of the Junior Algebra and Number Theory seminar series.

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