In the paper

auther proves maxmum normal perfect subgroup P(G) of a finite group G to be solvable superfluity of G

and dicusses some essen- cial properties of P(G). Useing these properties

author proves that a sufficient condition which finite group G is p-solvable in is (|P(G)|

p)=1

and the condition is necessary for p-nilpotent and p-supersolvable groups. In the end

author establishes a functor S between the category of finite group and the category of finite solvable group and discusses the exactness of S.