Center is direct projection-invariant

Statement
The center of a group is a direct projection-invariant subgroup: any projection to a direct factor sends the center to within itself.

Related subgroup properties satisfied by the center

 * Center is characteristic
 * Center is strictly characteristic
 * Center is quasiautomorphism-invariant

Related subgroup properties not satisfied by the center

 * Center not is fully characteristic
 * Center not is I-characteristic