Aims & Learning Objectives:
Aims: This course provides a solid introduction to modern group theory covering both the basic tools of the subject and more recent developments.
At the end of the course, students should be able to state and prove the main theorems of classical group theory and know how to apply these. In addition, they will have some appreciation of the relations between group theory and other areas of mathematics.
Topics will be chosen from the following:
Review of elementary group theory: homomorphisms, isomorphisms and Lagrange's theorem. Normalisers, centralisers and conjugacy classes. Group actions. p-groups and the Sylow theorems. Cayley graphs and geometric group theory. Free groups. Presentations of groups. Von Dyck's theorem. Tietze transformations.
THIS UNIT IS ONLY AVAILABLE IN ACADEMIC YEARS STARTING IN AN ODD YEAR.