Hypercentral group

Symbol-free definition
A group is said to be hypercentral (also, hypernilpotent) if its upper central series terminates at the whole group, or equivalently, if it equals its hypercenter.

Stronger properties

 * Nilpotent group

Weaker properties

 * Locally nilpotent group
 * Group in which every maximal subgroup is normal
 * Hyperabelian group