Second center contains Baer norm

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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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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

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