Module Specification
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
1. Module Title GROUP THEORY
2. Module Code MATH343
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 6 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr R Nair Mathematical Sciences Nair@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Professor A Pratoussevitch Mathematical Sciences Anna.Pratoussevitch@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 33

   11

     4

 48
17.

Private Study

 102
18.

TOTAL HOURS

 150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

 
24. Programme(s) (including Year of Study) to which this module is available on a mandatory basis:
25. Programme(s) (including Year of Study) to which this module is available on a required basis:
26. Programme(s) (including Year of Study) to which this module is available on an optional basis:
27. Aims
 

To introduce the basic techniques of finite group theory with the objective of explaining the ideas needed to solve classification results.
 
28. Learning Outcomes
 

(LO1) Understanding of abstract algebraic systems (groups) by concrete, explicit realisations (permutations, matrices, Mobius transformations).
 

(LO2) The ability to understand and explain classification results to users of group theory.
 

(LO3) The understanding of connections of the subject with other areas of Mathematics.
 

(LO4) To have a general understanding of the origins and history of the subject.
 

(S1) Problem solving skills
 

(S2) Logical reasoning
 
29. Teaching and Learning Strategies
 

Material is provided in advance of classes for students to study asynchronously. The contact hours consist of one 2-hour active learning session and one 2-hour supported study/drop-in session.

A week during the semester will be identified as a reading week for this module. During this week there is no in-class teaching, instead students are provided with structured materials to learn a relevant topic which is included in the exam. The lecturer will be available during the reading week for student queries during the usual lecture/tutorial hours for the module and also during the normal office hours.
 
30. Syllabus
   

- Definitions and examples.

- Cyclic, dyhedral and symmetric groups.

- Abelian groups. Orders of elements.

- Subgroups, cosets and Lagrange's Theorem.

- Normal subgroups and quotient groups.

- Automorphisms. Semi-direct products.

- The Homomorphism Theorem.

- The Orbit-Stabiliser Theorem.

- Mobius transformations.

- The Sylow Theory. Applications of Sylow Theory to classification problems.
 
31. Recommended Texts
  Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
 

Assessment
32. EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Final Exam There is a resit opportunity available. 120 70
33. CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  class test 60 30