Gruenberg group

Symbol-free definition
A group is said to be a Gruenberg group if every cyclic subgroup of it is ascendant.

Stronger properties

 * Weaker than::Nilpotent group
 * Weaker than::Group satisfying normalizer condition
 * Weaker than::Group in which every subgroup is subnormal

Weaker properties

 * Stronger than::Locally nilpotent group