Second center contains Baer norm

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.
View other such results

History

This result is due to Schenckman, and was proved in 1960. PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.

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

• Centralizer of derived subgroup contains Baer norm

Facts used

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