 If the inner automorphism group of a perfect group is simple, then is called quasisimple.An automorphism of a Lie algebra is called an inner automorphism if it is of the form , where is the adjoint map and is an element of a Lie group whose Lie algebra is .The notion of inner automorphism for Lie algebras is compatible with the notion for groups in the sense that an inner automorphism of a Lie group induces a unique inner automorphism of the corresponding Lie algebra.