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 $h(S)\ge 10$. If $h(S)<14$ then $A_5$ is the only simple factor. If $S$ is virtually nilpotent and $h(S)\le 14$ then its Fitting subgroup has nilpotency class $\le 3$.

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

AMS Subject Classification: Primary 20F16.