Local analysis of the normalizer problem

AbstractFor 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(G). Let Autint(G)=AutA(G), where A is the ring of all algebraic integers in C. It is shown how Clifford theory can be used to analyze Autint(G). 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 AutZ(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)≠Inn(G) is given