Csaba Schneider

Universida de Federal de Minas Gerais

The wreath product construction is an essential tool in permutation group theory. The wreath product of two permutation groups has two widely used actions (namely the imprimitive action and the product action) and understanding these actions is essential in reduction arguments for permutation groups. In several of the classes identified by the O'Nan-Scott Theorem for finite primitive and quasiprimitive groups, the members are constructed using a wreath product. The twisted wreath product is a generalization of the wreath product construction, and a number of important primitive or quasiprimitive permutation groups can be described as twisted wreath products. In these lectures, we will review the most important properties of wreath products and twisted wreath products. I will present necessary and/or sufficient conditions for the primitivity or quasiprimitivity of such wreath products. We will treat the following topics in more detail: