Topics

Introduction: permutation groups, group actions, and “base and strong generating set”

The O’Nan Scott theorem and methods for the classification of primitive permutation groups

Aschbacher’s Theorem and computational methods for matrix groups

Random generation of groups

Primitive and quasiprimitive - lessons from algebraic graph theory (distance transitive graphs and normal graph quotients)

Theory of Quasiprimitive permutation groups - and normal quotients of edge-transitive graphs

Overview of simple groups factorisations and their applications, especially to classify the maximal subgroups of symmetric groups

Growth of groups (Pyber, Tao et al) and conjectures of Sims and Weiss for arc-transitive graphs

Deterministic and randomised algorithms in group theory

Proportions of elements in permutation groups and matrix groups, estimation methods

Computational methods for permutation groups

Growth of subgroups: Sylow subgroups of primitive permutation groups