COLEMAN AUTOMORPHISMS OF STANDARD WREATH PRODUCTS OF NILPOTENT GROUPS BY GROUPS WITH PRESCRIBED SYLOW 2-SUBGROUPS

Abstract

Let G = N wr H be the standard wreath product of N by H, where N is a finite nilpotent group and H is a finite group whose Sylow 2-subgroups are either cyclic, dihedral or generalized quaternion. It is shown that every Coleman automorphism of G is inner. As a direct consequence of this result, it is obtained that the normalizer property holds for G.