Second center contains Baer norm

History
This result is due to Schenckman, and was proved in 1960. 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) uses::Cooper's theorem: Cooper's theorem states that every power automorphism centralizes every inner automorphism.