Bases for primitive permutation groups

Abstract: The notion of a base for a permutation group is a fundamental concept in permutation group theory. The minimal cardinality of a base is called the base size of the group. Determining this invariant is a fundamental problem in permutation groups, with a long history stretching back to the nineteenth century. We will introduce the main motivations to study the base size, and we will recall some key results about this invariant. We will define the concepts of irredundant bases and we will explain the connection between these bases and the bases of minimal cardinality. We will also review some results about primitive permutation groups having all irredundant bases ofthe same size.

group theoryrings and algebras

Audience: researchers in the topic

Al@Bicocca take-away