Idempotent subgroup-defining function

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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

Definition with symbols

A subgroup-defining function f is said to be idempotent if for any group G, f(f(G)) = f(G) (that is, they both refer to the same subgroup of G).

Relation with other properties

Subgroup-defining functions satisfying this property

A full listing is available at:

Category:Idempotent subgroup-defining functions

Center

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.