# Hirsch length of virtually polycyclic group

Denote the Hirsch length of a group $G$ by $h(G)$. Let $G$ be a virtually polycyclic group and let $H$ be a normal subgroup of $G$. I am not sure how to prove that $h(G)=h(G/H)+h(H)$.

I know the above relation is quite trivial in the polycyclic case, but I do not know how to deal with the virtually polycyclic case. I hope someone can help me.

## migrated from mathoverflow.netJul 18 '18 at 14:30

This question came from our site for professional mathematicians.

• Firstly, this is a standard result, not a research problem. Secondly, people might be more inclined to help if you explained exactly where you were stuck. – Derek Holt Jul 7 '18 at 9:02