Covering group

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 $$E$$.

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.