Coleman automorphisms of permutational wreath products II

Let K be an arbitrary permutation group on a finite set Ω. Let G = H≀K be the corresponding permutational wreath product of a group H by K. It is proved that every Coleman automorphism of G is inner whenever H is either an almost simple group or a p-constrained group with Op′(H)=1 for some prime p. In particular, the normalizer conjecture holds for such groups G. Other positive results regarding the normalizer conjecture are also obtained. Our results extend some known ones.