Author: 

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

Fax: (49 711)685-5304

Title:

Local analysis of the normalizer problem

Abstract:

For a finite group $G$, and a commutative ring $R$,
the automorphisms of $G$ inducing an inner automorphism of the group ring $RG$
form a group $\autR{R}{G}$. Let $\autint{G}=\autR{A}{G}$, where $A$ is the 
ring of all algebraic integers in $\CC$. Testing some $\sigma\in\aut{G}$ for 
membership of $\autint{G}$ is a total issue for localization,
and then Clifford theory provides a powerful tool.
It is proved that $\autint{G}/\inn{G}$ is an abelian group, 
and can indeed be any finite abelian group.
It is an outstanding question whether $\autR{\sZZ}{G}=\inn{G}$ if 
$G$ has an abelian Sylow $2$-subgroup. 
This is shown to be true in some special cases, 
but also a group $G$ with abelian Sylow subgroups and 
$\autint{G}\neq\inn{G}$ is given.

Current status: submitted for publication