Course Catalogue

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The aim of this course is to study some advanced topics in group theory and applications thereof.

2 hours of lectures a week, over 11 weeks.

1 hour tutorial a week over 10 weeks (or equivalent)

Mandatory Entry Requirements

4H Topics in Algebra.

Assessment

100% Final Exam

Reassessment

In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

The aim of this course is to study some advanced topics in group theory and applications thereof. Typically the lecturer will focus either on geometric and combinatorial group theory or on the theory and applications of linear representations of finite groups.

By the end of this course students will be able to:

• Demonstrate knowledge of the central definitions and facts of selected topics in advanced group theory and use these to solve problems of a numerical or logical nature. Specific topics include one of:

1. Geometric and combinatorial group theory (Cayley graphs, trees, properties of infinite discrete groups, decision problems, product constructions)

2. Linear representations of finite groups (character theory, induced representations, Artin's theorem, Brauer's theorem, Burnside's p^a q^b theorem, applications to number theory)

• Apply operator-algebraic techniques to reformulate and solve group-theoretic problems (group C*-algebras, amenability, Zalesski's theorem, Baum-Connes conjecture).

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.