Programme And Module Handbook
 
Course Details in 2025/26 Session


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Module Title LH Group Theory
SchoolMathematics
Department Mathematics
Module Code 06 29727
Module Lead Dr Corneliu Hoffman
Level Honours 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) Linear Algebra - (06 15552)
Co-requisites
Restrictions Prohibited module combination: 22519 LM Group Theory
Contact Hours Lecture-46 hours
Seminar-10 hours
Guided independent study-144 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 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
Assessment 29727-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions "Assessments: 2 hour Summer Examination (80%); In-course Assessment (20%). "
Other
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