on marginal automorphisms of a group fixing the certain subgroup

Let w be a variety of groups defined by a set w of laws and g be a finite pgroup in w. the automorphism α of a group g is said to bea marginal automorphism (with respect to w), if for all x ∈ g, x^−1α(x) ∈ w∗(g), where w∗(g) is the marginal subgroup of g. let m,n be two normalsubgroups of g. by autm(g), we mean the subgroup of aut(g) consistingof all automorphisms which centralize g/m. autn(g) is used to show thesubgroup of aut(g) consisting of all automorphisms which centralize n. we denote autn(g)∩autm(g) by autmn (g). in this paper, we obtain a necessary and sufficient condition that autw∗ (g) = autw∗(g)w∗(g)(g).