Coleman automorphisms of finite groups

An automorphism of a finite group G whose restriction to any Sylow subgroup equals the restriction of some inner automorphism of G shall be called Coleman automorphism, named for D. B. Coleman, who's important observation from [2] especially shows that such automorphisms occur naturally in the study of the normalizer of G in the units of the integral group . Let Out be the image of these automorphisms in Out. We prove that Out is always an abelian group (based on previous work of E. C. Dade, who showed that Out is always nilpotent). We prove that if no composition factor of G has order p (a fixed prime), then Out is a -group. If O, it suffices to assume that no chief factor of G has order p. If G is solvable and no chief factor of has order 2, then , where is the center of . This improves an earlier result of S. Jackowski and Z. Marciniak. Received: 26 May 2000; in final form: 5 October 2000 / Published online: 19 October 2001