Group in which every cyclic subgroup is 2-subnormal

Symbol-free definition
A group in which every cyclic subgroup is 2-subnormal is a group with the property that every cyclic subgroup (i.e., the subgroup generated by any subset of the group) of the group is a 2-subnormal subgroup.

Stronger properties

 * Weaker than::Abelian group
 * Weaker than::Dedekind group
 * Weaker than::Group of nilpotence class two
 * Weaker than::Group in which every subgroup is 2-subnormal

Weaker properties

 * Stronger than::3-Engel group:
 * Stronger than::Gruenberg group