# Second center contains Baer norm

From Groupprops

This article gives the statement, and possibly proof, of the subgroup obtained from one subgroup-defining function, namely Baer norm, always being contained in the subgroup obtained from another subgroup-defining function, namely second center.

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## Contents

## History

This result is due to Schenckman, and was proved in 1960.**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE] It follows from Cooper's theorem.

## Statement

The second center of a group, i.e., the second member of its upper central series, contains the Baer norm of the group, i.e., the intersection of the normalizers of all the subgroups.

## Related facts

## Facts used

- Cooper's theorem: Cooper's theorem states that every power automorphism centralizes every inner automorphism.