Center is characteristic

Statement
The center of a group is a characteristic subgroup of it.

Stronger facts: stronger subgroup properties satisfied
The center satisfies a number of stronger properties:

Weaker facts: weaker subgroup properties satisfied

 * Stronger than::Center is normal

Analogues in other algebraic structures

 * Center is characteristic for Lie rings
 * Center is derivation-invariant (another analogue for Lie rings)