Author: 

Dr.~M.~Hertweck, Universit\"at Stuttgart, Pfaffenwaldring 57, 
D-70550 Stuttgart, Germany 

Fax: (49 711)685-5304

Title:

Class-preserving automorphisms of finite groups

Abstract:

We construct a family $\mathcal{F}$ of Frobenius groups having abelian 
Sylow subgroups and non-inner, class-preserving automorphisms. We show that
any A-group (that is, a finite solvable group with abelian Sylow subgroups)
has a section belonging to $\mathcal{F}$ provided it has a
non-inner, class-preserving automorphism.
As a consequence, we obtain
that for metabelian A-groups, or A-groups with elementary abelian 
Sylow subgroups, class-preserving automorphisms are necessarily inner
automorphisms. The same is true for a finite group 
whose Sylow subgroups of odd order are all 
cyclic, and whose Sylow $2$-subgroups are either cyclic, dihedral or 
generalized quaternion. Some applications are given.

Current status: submitted for publication