  We investigate finite groups with the Magnus Property, where a group is said
to have the Magnus Property (MP) if whenever two elements have the same normal
closure then they are conjugate or inverse conjugate. In particular we observe
that a finite MP group is solvable, determine the finite primitive MP groups
and determine all the possible orders of the chief factors of a finite MP
group. We also determine the MP finite direct products of finite primitive
groups, as well as the MP crown-based powers of a finite monolithic primitive
group.
