Year: 2023
Type: preprint
Abstract: We prove that a map onto a nilpotent group $Q$ has finitely generated kernel if and only if the preimage of the positive cone is coarsely connected as a subset of the Cayley graph for every full archimedean partial order on $Q$. In case $Q$ is abelian, we recover the classical theorem that $N$ is finitely generated if and only if $S(G,N) \subseteq Σ^1(G)$. Furthermore, we provide a way to construct all such orders on nilpotent groups. A key step is to translate the classical setting based on characters into a language of orders on $G$.
Source: arXiv (Cornell University)
Author: Klinge, Kevin
Institution: Karlsruhe Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388276194