Nilpotent injectors in finite groups

In [3] A. Bialostocki has introduced a special das's of maximal nilpotent s ubgroups in an arbitrary finite group. In this paper we want to investigate the relationship between this special class of maximal nilpotent subgroups and the more classical N-injectors in an arbitrary finite group. To do this we prove the following theorem which is of fundamental importanc e in this investigation: Let U be a nilpotent subgroup of G containing every U-invariant nilpotent s ubgroup of G. Then U is an N-injector of G.