# Center is bound-word

From Groupprops

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.

## 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`