Section outline

  • This week we will introduce the notion of an action of a group, which is of fundamental importance when applying group theory to problems in other areas of mathematics such as geometry and combinatorics. We will introduce the notions of orbit and stabiliser and prove the Orbit-Stabiliser Theorem, which is one of the most useful results in the course in terms of applications. We will consider some applications of the orbit-stabiliser theorem to counting problems in combinatorics and linear algebra, and also apply it to study the symmetry groups of geometric objects. This activity may continue into the early part of Week 10.

    This week we expect to cover most or all of section 5 of the notes.

    At the end of this week you will be able to use the Week 9 Quiz.