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Module Title Group Theory and Galois Theory
SchoolMathematics
Department Mathematics
Module Code 06 22500
Module Lead S Shpectorov
Level Honours Level
Credits 20
Semester Full Term
Pre-requisites LI Linear Algebra & Linear Programming - (06 25765) LH Algebra & Combinatorics 2 - (06 27142) Linear Algebra - (06 15552) LI Algebra & Combinatorics 2 - (06 25665)
Co-requisites
Restrictions None
Contact Hours Lecture-46 hours
Seminar-0 hours
Tutorial-10 hours
Project supervision-0 hours
Demonstration-0 hours
Practical Classes and workshops-0 hours
Supervised time in studio/workshop-0 hours
Fieldwork-0 hours
External Visits-0 hours
Work based learning-0 hours
Guided independent study-0 hours
Placement-0 hours
Year Abroad-0 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 Jordan-Holder theorem makes this statement precise) and these will be studied. The alternating groups and linear groups will be introduced as first examples of non-abelian simple groups.
Later in the course field automorphisms may be considered so that an overview of Galois Theory can be given.
is related to the structure of the field extension via the Fundamental Theorem of Galois Theory
Learning Outcomes By the end of the module the student will 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 Jordan-Holder theorem.
Assessment 22500-01 : Raw Module Mark : Coursework (0%)
22500-03 : Final Module Mark : Coursework (100%)
Assessment Methods & Exceptions Assessments: 22500-01: Exam : Exam (CT) - Written Unseen (90%)
22500-02 : Continuous Assessment : Coursework or class Tests (10%)
Other None
Reading List