Title: On the Transfer Map

Abstract:  Let G be a finite group and let H be a group of finite index. Then there is a nice way of defining a homomorphism from G to H/H’. This map is ubiquitous in group theory. A bit more surprisingly, it shows up in other areas of mathematics such as in Class Field Theory, Algebraic Topology and classical number theory. We will study the transfer map, and get some information on how the Sylow subgroups of a finite group G control the structure of G using transfer theory. We will also talk about a really neat application in number theory.