Non-solvable torsion-free virtually solvable groups

Jonathan A. Hillman

Abstract

We show that a non-solvable, torsion-free, virtually solvable group \(S\) must have Hirsch length \(h(S)\geq10\). If \(h(S)<14\) then \(A_5\) is the only simple factor. If \(S\) is virtually nilpotent and \(h(S)\leq14\) then its Fitting subgroup has nilpotency class \(\leq3\).

Keywords: Hirsch length, nilpotent, non-solvable, perfect, simple,torsion-free, virtually polycyclic.

AMS Subject Classification: Primary 20F16.