Module Title  LM Group Theory 
School  Mathematics 
Department  Mathematics 
Module Code  06 35167 
Module Lead  Sergey Shpectorov 
Level  Masters Level 
Credits  20 
Semester  Semester 2 
Prerequisites 
LH Algebra & Combinatorics 2  (06 27142)
LI Linear Algebra & Linear Programming  (06 25765)
LI Algebra & Combinatorics 2  (06 25665)

Corequisites 

Restrictions  Prohibited module combinations: 22500 LM Group Theory 
Exclusions  
Description  Group theory is the mathematical study of symmetry. In this course groups and their actions on sets, and geometric structures will be studied. A highlight of this course is Sylow's Theorem, which is probably the most fundamental results about the structure of finite groups. Finite simple groups are the building blocks from which all finite groups are built (the JordanHolder theorem makes this statement precise) and these will be studied. The alternating groups and linear groups will be introduced as first examples of nonabelian simple groups.
Later in the course field automorphisms may be considered so that an overview of Galois Theory can be given. 
Learning Outcomes  By the end of the module students should be able to:  Understand and apply the theory of groups and group actions and calculate in examples
 Understand the concepts of homomorphism, isomorphisms and quotient groups
 Analyse the structure of groups using Sylow’s theorem and other results from the course, for example, the JordanHolder theorem
 Level M students will explore the subject beyond the taught syllabus

Assessment 
3516701 : Raw Module Mark : Coursework (100%)

Assessment Methods & Exceptions  Assessments: 2 hour Summer Examination (80%); Incourse Assessment (20%). 
Other  
Reading List 
