Solvable normal subgroups of 2-knot groups

Abstract

If [Formula: see text] is an orientable, strongly minimal [Formula: see text]-complex and [Formula: see text] has one end, then it has no nontrivial locally finite normal subgroup. Hence, if [Formula: see text] is a 2-knot group, then (a) if [Formula: see text] is virtually solvable, then either [Formula: see text] has two ends or [Formula: see text], with presentation [Formula: see text], or [Formula: see text] is torsion-free and polycyclic of Hirsch length 4 (b) either [Formula: see text] has two ends, or [Formula: see text] has one end and the center [Formula: see text] is torsion-free, or [Formula: see text] has infinitely many ends and [Formula: see text] is finite, and (c) the Hirsch–Plotkin radical [Formula: see text] is nilpotent.