Coleman Since Isomorphic Results

Coleman automorphism occurred first in the study of the normalizer Nu(rg) (G) of G in the units U{RG) of RG.In research of the normalizer,when R =Z,the case must be considered specially. Thus the class of groups with (NP)(see Introduction) need to be researched.Through the study of Coleman automorphism, more informations on the group may be obtained.E.C.Dade made enormous researches on Coleman automorphism of a finite group and obtained a lot of initial results,especially proved that Coleman outer automorphism group is nilpotent.Recently,M.Hertweck and W.Kimmerle proved that Coleman outer automorphism group is abelian and gave some sufficient conditions on the group being a p — group and trivial group.In the paper,Coleman automorphism is further researched and some properties of Coleman automorphism are obtained.Furthermore,by the properties some sufficient conditions on Cole-man outer automorphism group being a p — group are also obtained,where the sufficient conditions are different from the results of M.Hertweck and W.Kimmerle.By the foregoing re-sults,some conclusions on Coleman outer automorphism group being trivial are drawn.Enormous examples incarnate the results.