Central extension

Definition

A central extension is a group extension where the base normal subgroup is a central subgroup, i.e., it is contained in the center of the whole group.

Central extensions are significant because the central extensions for a given normal subgroup and quotient group are classified by the second cohomology group for trivial group action of the quotient group on the normal subgroup.

Properties

• Stem extension
• Split central extension
• Perfect central extension
• Universal central extension