Group Theory and Galois Theory

School of Mathematics

College of Engineering and Physical Sciences

Details

Code 22500

Level of study Third/Final year

Credit value 20

Semester Students may study either 1, 2 (providing they have familiarity with the material from 1) or both.

Pre-requisite modules 22503,22507

Module description

Semester 1: The highlight of this Group Theory module is Sylow's Theorem, which is probably the most fundamental result about the structure of finite groups. The Jordan - Holder Theorem shows that simple groups are the building blocks from which other groups are built, while alternating groups are also provided as the first examples of non-abelian simple groups.

Semester 2: Galois theory studies field extensions, particularly those arising from adjoining roots of polynomials. To each field extension we associate the Galois group. The structure of the group is related to the structure of the field extension via the Fundamental Theorem of Galois Theory.

Teaching and learning methods

Lectures.