journal of Groups, Complexity, Cryptology

Authors: Gemma Crowe ^1,2

• 1 University of Manchester
• 2 Heilbronn Institute for Mathematical Research

In this paper we provide an alternative solution to a result by Juhász that the twisted conjugacy problem for odd dihedral Artin groups is solvable, that is, groups with presentation $G(m) = \langle a,b \; | \; _{m}(a,b) = {}_{m}(b,a) \rangle$, where $m\geq 3$ is odd, and $_{m}(a,b)$ is the word $abab \dots$ of length $m$, is solvable. Our solution provides an implementable linear time algorithm, by considering an alternative group presentation to that of a torus knot group, and working with geodesic normal forms. An application of this result is that the conjugacy problem is solvable in extensions of odd dihedral Artin groups.

Published in the journal of Groups, Complexity, Cryptology