Abstract. Given an element x of a group G, let N_x be the (normal) subgroup generated by the conjugacy class of x in G. A group G is said to have the Magnus property if, whenever two elements x,y of G satisfy N_x = N_y, the two elements x,y are either conjugate or inverse-conjugate in G. Free groups have this property. In a recent paper (available on arxiv), Benjamin Klopsch, Luis Mendonça and Jan Moritz Petschick proved several results concerning groups with the Magnus property, including the fact that, if the group G satisfies some "finiteness" condition, then having the Magnus Property passes to quotients. In particular, this holds for finite groups. In this talk I will discuss some recent results about finite groups with the Magnus property. We will focus specifically on primitive groups and the structure of the factor group modulo the Frattini subgroup. This is a joint work with Claude Marion (University of Porto).