# Baer norm is strictly characteristic

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., Baer norm) always satisfies a particular subgroup property (i.e., strictly characteristic subgroup)}

View subgroup property satisfactions for subgroup-defining functions View subgroup property dissatisfactions for subgroup-defining functions

## Statement

The Baer norm of a group (defined as the intersection of the normalizers of all its subgroups) is a strictly characteristic subgroup: any surjective endomorphism of the whole group maps it to within itself.