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Sigma invariants for partial orders on nilpotent groups
- Publication Year :
- 2023
-
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 $S(G,N) \subseteq \Sigma^1(G)$. 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 $G$.<br />Comment: 21 pages, comments welcome
- Subjects :
- Mathematics - Group Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2311.00620
- Document Type :
- Working Paper