Year: 2024
Type: article
Abstract: A group 𝐺 is twisted conjugacy separable if, for every automorphism 𝜑, distinct 𝜑-twisted conjugacy classes can be separated in a finite quotient. Likewise, 𝐺 is completely twisted conjugacy separable if, for any group 𝐻 and any two homomorphisms φ , ψ \varphi,\psi from 𝐻 to 𝐺, distinct ( φ , ψ ) (\varphi,\psi) -twisted conjugacy classes can be separated in a finite quotient. We study how these properties behave with respect to taking subgroups, quotients and finite extensions, and compare them to other notions of separability in groups. Finally, we show that, for polycyclic-by-nilpotent-by-finite groups, being completely twisted conjugacy separable is equivalent to all quotients being residually finite.
Source: Journal of Group Theory
Author: Sam Tertooy
Institution: KU Leuven
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405016173