Algorithms for twisted conjugacy classes of polycyclic-by-finite groups II
arXiv:2504.03596 · doi:10.1016/j.jalgebra.2026.03.044
Abstract
We construct an algorithm that, given a pair of homomorphisms between polycyclic-by-finite groups, determines whether their Reidemeister number is finite, and if so returns a set of representatives of the twisted conjugacy classes. Moreover, we show how this algorithm can be applied to compute double cosets and orbits of affine actions.
v3: accepted manuscript. v2: rewritten sections 1-8 + added sections on double cosets and affine actions. 17 pages, comments welcome!