Center is bound-word

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., bound-word subgroup)}
View subgroup property satisfactions for subgroup-defining functions $|$ View subgroup property dissatisfactions for subgroup-defining functions

Statement

The center of a group is a bound-word subgroup: it can be expressed as the union of sets of solutions to systems of equations in the group, where all other variables are existentially or universally quantified.

Related facts

• Center is strictly characteristic: For full proof, refer: center is strictly characteristic
• Members of the finite part of the upper central series: For full proof, refer: upper central series members are bound-word