Programme And Module Handbook
Course Details in 2025/26 Session

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Module Title LM Group Theory
Department Mathematics
Module Code 06 35167
Module Lead Sergey Shpectorov
Level Masters Level
Credits 20
Semester Semester 2
Pre-requisites LH Algebra & Combinatorics 2 - (06 27142) LI Linear Algebra & Linear Programming - (06 25765) LI Algebra & Combinatorics 2 - (06 25665)
Restrictions Prohibited module combinations: 22500 LM Group Theory
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.
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 Jordan-Holder theorem
  • Level M students will explore the subject beyond the taught syllabus
Assessment 35167-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions Assessments: 2 hour Summer Examination (80%); In-course Assessment (20%).
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