Module Title  LH Group Theory 
School  Mathematics 
Department  Mathematics 
Module Code  06 29727 
Module Lead  Dr Corneliu Hoffman 
Level  Honours 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)
Linear Algebra  (06 15552)

Corequisites 

Restrictions  Prohibited module combination: 22519 LM Group Theory 
Contact Hours 
Lecture46 hours
Seminar10 hours
Guided independent study144 hours
Total: 200 hours

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

Assessment 
2972701 : Raw Module Mark : Coursework (100%)

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