Idempotent subgroup-defining function
This article defines a property of subgroup-defining functions, viz., a property that any subgroup-defining function may either satisfy or not satisfy
This article defines a notion of an idempotent (one that equals its square) in a certain context
Definition with symbols
A subgroup-defining function is said to be idempotent if for any group , (that is, they both refer to the same subgroup of ).
Relation with other properties
Subgroup-defining functions satisfying this property
A full listing is available at:
The center of the center of a group is again the center.
Any group that arises as the center of some group must be Abelian, and any Abelian group is its own center.