Abstract

This project is going to be based on the transfer of finite groups. Briefly defined as such:

Let G be a group, let H and K be sub groups of G such that K is a normal subgroup of H and the factor group H/K is abelian.
Then the homomorphism A: G -> H/K is called the transfer.*

This transfer was first used to help prove Burnside's Theorem and was used in the specific case of mononomials. Another famous case this has been used in is the Gauss Lemma on quadratic residue**. The transfer has been used to help with many proofs, allowing to gain insight in to the group which is apparently difficult through other means.

In this project, the transfer and any preceding concepts will be formally defined. Examples of the transfer, its properties and characteristics will then be discussed. With the possibility at the end there will be a further discussion on various modern developments and usage of the transfer that of occurred in the latter half of the 20th century onwards.


*Definition comes from "Group Theory" by Michia Suzuki
** Example comes from the '13:13, 23 September 2006' edition of the Wikipedia page "Transfer (group theory)".