- The center of the join of abelian subgroups of maximum order in .
- The intersection of the abelian subgroups of maximum order.
The term ZJ-functor is also used for this because the subgroup-defining function is a characteristic p-functor: it always returns a nontrivial characteristic subgroup for any nontrivial group of prime power order.
The letters ZJ are used because Z denotes the center and J denotes the join of abelian subgroups of maximum order (also called the Thompson subgroup). The result of applying the ZJ-functor to a group is denoted or .