Algorithms for twisted conjugacy classes of polycyclic-by-finite groups II

2025/04/04 by Tertooy, Sam
#20-08 (Primary) 20E45 #20F10 #20F19 (Secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2504.03596

Abstract

We construct an algorithm that, given a pair of homomorphisms between polycyclic-by-finite groups, determines whether their Reidemeister number is finite, and additionally returns a set of representatives of the twisted conjugacy classes if it is. Moreover, we show how this algorithm can be applied to compute double cosets and orbits of affine actions.

Related

• Twisted conjugacy classes for polyfree groups
• Twisted conjugacy separable groups
• Twisted Burnside theorem for type II₁ groups: an example
• Twisted Burnside-Frobenius theory for discrete groups
• Reidemeister number of any automorphism of a Gromov hyperbolic group is infinite