Hypocentral group

Definition
A group is said to be hypocentral if its lower central series terminates at the identity, or equivalently, if its hypocenter is the trivial group.

Stronger properties

 * Nilpotent group: Here, the lower central series terminates at the identity in finitely many steps, the number of steps being the nilpotence class.
 * Residually nilpotent group: Here, the intersection of the finite terms of the lower central series is the trivial group.

Weaker properties

 * Locally nilpotent group
 * Hypoabelian group