SOME SUFFICIENT CONDITIONS FOR THE COLEMAN OUTER AUTOMORPHISM GROUP OF A FINITE GROUP BEING A p'-GROUP

In this paper,the problem for the Coleman outer automorphism group of a finite group G to be a p'-group is studied.By using some properties of Sylow p-subgroups and homology groups,we obtain some sufficient conditions for the Coleman outer automorphism group of a finite group being a p'-group.Our results are different from those of M.Hertweck and W.Kimmerle.