2-locally nilpotent group

Definition
A group is termed a 2-locally nilpotent group if every 2-generated subgroup of it is a nilpotent group.

The 2-local nilpotency class of a 2-locally nilpotent group is defined as the supremum, over all 2-generated subgroups, of their nilpotency class. The 2-local nilpotency class of a 2-locally nilpotent group may be infinite. An example is the generalized dihedral group for 2-quasicyclic group.