Center is normal

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This article gives the statement, and possibly proof, of the fact that for any group, the subgroup obtained by applying a given subgroup-defining function (i.e., center) always satisfies a particular subgroup property (i.e., normal subgroup)}
View subgroup property satisfactions for subgroup-defining functions | View subgroup property dissatisfactions for subgroup-defining functions

Statement

The center of any group is a normal subgroup.

Related facts

More about the center

Stronger subgroup properties satisfied

Stronger subgroup properties not satisfied