ABSTRACT
In [6] Gaschu¨tz introduced the notion of crown associated with a complemented chief factor H/K of a finite soluble group G; the crown is a certain normal factor of G, which collects all complemented chief factors of G which are G-isomorphic to H/K. He employed this notion in the construction of a characteristic conjugacy class of subgroups, the prefrattini subgroups. Later this notion has been generalized to all finite groups (see for example [10] and [8]): it has been defined the crown associated with a non-Frattini chief factor of an arbitrary finite group.
