Covering group

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Template:Central extension property

Definition

Symbol-free definition

A covering group of a group is defined as a central extension that is perfect as a group.

Definition with symbols

Let G be a group. A covering group for G is a perfect group E along with a map \rho: E \to G such that the kernel of \rho lies inside the center of E.

Related group properties

For a simple group

Any covering group of a simple group is a quasisimple group. Further, it is true that the universal covering group of a simple group is a finite quasisimple group.