Virtually nilpotent group

Definition
A group is termed virtually nilpotent if it satisfies the following equivalent conditions:


 * 1) It has a subgroup of finite index that is nilpotent.
 * 2) It has a normal subgroup of finite index that is nilpotent.
 * 3) There is a surjective homomorphism from it to a finite group such that the kernel is a nilpotent normal subgroup.
 * 4) There is a homomorphism from it to a finite group such that the kernel is a nilpotent normal subgroup.

Stronger properties

 * Weaker than::Virtually abelian group

Weaker properties

 * Stronger than::Virtually solvable group