MATH40410 Group Theory

Academic Year 2021/2022

The main objective of this module is to investigate the structure of finite groups and hence to classify groups of a given order up to isomorphism.

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Curricular information is subject to change

Learning Outcomes:

The student will be able to understand some of the following concepts:

(i) Abelian groups: the classification of finite abelian groups.
(ii) Permutation groups: permutations, orbit-stabilizer theorem, Cayley's theorem, A(5) is simple.
(iii) Sylow's theorems: double cosets, Sylow's theorems, some consequences of Sylow's theorems, applications of Sylow's theorems.
(iv) Jordan-Holder theorem: direct products, Schreier's refinement theorem, Jordan-Holder theorem, characteristically simple groups.
(v) Soluble groups: definitions, derived groups, characterizing certain groups of small order.

Indicative Module Content:

Student Effort Hours: 
Student Effort Type Hours
Lectures

24

Tutorial

12

Specified Learning Activities

24

Autonomous Student Learning

50

Total

110

Approaches to Teaching and Learning:
Lectures, tutorials and problem solving. 
Requirements, Exclusions and Recommendations
Learning Requirements:

MATH10040
MATH20310


Module Requisites and Incompatibles
Required:
MATH10040 - Numbers & Functions, MATH20310 - Groups, Rings and Fields


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: Examination 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

70

Assignment: Homework Throughout the Trimester n/a Standard conversion grade scale 40% No

30


Carry forward of passed components
No
 
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Solutions to homework problems will be covered in tutorials. A practice examination will be covered at the end of the trimester.

A Course in Group Theory, J. F. Humphreys, Oxford Science Publications, ISBN 0198534590