MX3020: GROUP THEORY (2021-2022)

Last modified: 31 May 2022 13:05

Course Overview

Group theory concerns the study of symmetry. The course begins with the group axioms, which provide an abstract setting for the study of symmetry. We proceed to study subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Composition series are introduced and the Jordan-Holder theorem is proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout symmetric groups are consulted as a source of examples.

Course Details

Study Type	Undergraduate	Level	3
Term	First Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	Aberdeen	Sustained Study	No
Co-ordinators	Dr William Turner

Qualification Prerequisites

Either Programme Level 3 or Programme Level 4

What courses & programmes must have been taken before this course?

Either MA2008 Linear Algebra I (Passed) or MA2506 Linear Algebra (Passed)
Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

Course Description

Group axioms, subgroups, examples of groups.
Cosets of a subgroup
Lagrange's Theorem.
Homomorphisms, isomorphisms, normal subgroups, quotient groups.
Calculations in symmetric and alternating groups.
Group actions.
Sylow's Theorems.

Syllabus

Lagrange’s theorem
Symmetric groups and alternating groups.
Cyclic groups and their subgroups.
Homomorphisms and isomorphisms.
Normal subgroups and their quotient groups.
The three isomorphism theorems.
Simple groups and composition series. The Jordan-Holder theorem.
Group actions. The orbit-stabiliser theorem.
Sylow's theorems.
The classification of finite abelian groups

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

4x Assignments (20%, 20%, 20%, 40%)

Alternative Resit Arrangements

Resubmission of failed elements (pass marks carried forward)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge Level	Thinking Skill	Outcome
Factual	Remember	ILO’s for this course are available in the course guide.