The synchronisation hierarchy for permutation groups

Abstract: The concept of a synchronising permutation group was introduced nearly 15 years ago as a possible way of approaching The \v{C}ern\'y Conjecture. Such groups must be primitive. In an attempt to understand synchronising groups, a whole hierarchy of properties for a permutation group has been developed, namely, 2-transitive groups, $\mathbb{Q}$I-groups, spreading, separating, synchronising, almost synchronising and primitive. Many surprising connections with other areas of mathematics such as finite geometry, graph theory, and design theory have arisen in the study of these properties. In this survey talk I will give an overview of the hierarchy and discuss what is known about which groups lie where.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle