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Group Theory


  • Credit value: 15 credits at Level 7
  • Assessment: a three-hour examination (80%) and short, problem-based assignments (20%)

Module description

This module introduce you to further topics in group theory, extending and building on material covered at undergraduate level. It is a stand-alone course but will also give you experience in the subject at postgraduate level which will be useful if you are intending to pursue research in this area.

indicative module Syllabus

  • Group actions and G-sets; the Orbit-Stabilizer Theorem; application of G-sets to the proof of Sylow’s Theorems; use of Sylow’s Theorems to investigate groups of finite order; discussion of simple groups
  • Direct products of groups; groups which are the direct product of their Sylow subgroups; classification of finite abelian groups as direct products of certain cyclic groups
  • Revision of quotient groups; the three Isomorphism Theorems; normal series, composition series, chief series; the Jordan-Holder Theorem; composition factors and chief factors; definition of soluble groups; showing that a given group is or is not soluble; examples

Learning objectives

By the end of this module, you will have:

  • knowledge and understanding of, and the ability to use, mathematical techniques
  • knowledge and understanding of a range of results in mathematics
  • a deeper understanding of several topics in mathematics
  • the ability to comprehend and evaluate conceptual and abstract material
  • the ability to devise rigorous mathematical proofs
  • the ability to understand and apply mathematical reasoning in several different areas of mathematics
  • problem-solving skills, including the ability to assess problems logically and to approach them analytically.