Twisted conjugacy in dihedral Artin groups I: Torus Knot groups

2024/03/25 by Crowe, Gemma · 2 citations
#20F10 #20F36 #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2403.16671

Abstract

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) = ⟨ a,b | _m(a,b) = _m(b,a) ⟩, where m≥ 3 is odd, and _m(a,b) is the word abab … 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.

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• Twisted commutativity and conjugacy ratio in groups
• Twisted conjugacy in BS(n, 1)

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