Title of article :
Local analysis of the normalizer problem
Author/Authors :
Martin Hertweck، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2001
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(G). Let Autint(G)=AutA(G), where A is the ring of all algebraic integers in image. 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 image 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.
Journal title :
Journal of Pure and Applied Algebra
Journal title :
Journal of Pure and Applied Algebra