Module Details
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.
Title GROUP THEORY
Code MATH343
Coordinator Dr R Nair
Mathematical Sciences
Nair@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2021-22 Level 6 FHEQ First Semester 15

Aims

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

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

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.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Final Exam 6 questions of equal weight. The student will be assessed on their best five solutions. There is a resit opportunity available if required.  1 hour time on task    50       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
class test 1  60-90 minutes    25       
class test 2  around 60-90 minutes    25