Solvable normal subgroups of 2-knot groups
Geometric Topology
2021-02-24 v3
Abstract
If is an orientable, strongly minimal -complex and has one end then it has no nontrivial locally-finite normal subgroup. Hence if is a 2-knot group then (a) if is virtually solvable then either has two ends or , with presentation , or is torsion-free and polycyclic of Hirsch length 4; (b) either has two ends, or has one end and the centre is torsion-free, or has infinitely many ends and is finite; and (c) the Hirsch-Plotkin radical is nilpotent.
Keywords
Cite
@article{arxiv.1610.06629,
title = {Solvable normal subgroups of 2-knot groups},
author = {J. A. Hillman},
journal= {arXiv preprint arXiv:1610.06629},
year = {2021}
}
Comments
The introduction has been extended and there is a new section (partly speculative) on 2-knot groups of geometric dimension 2