2013 PhD Summer School in Discrete Mathematics - Minicourse III

MINICOURSE 3:  Imprimitive Permutation Groups

Speaker:  Prof. Edward T. Dobson, Mississippi State University, USA & UP, Slovenia

Abstract:

With the Classification of the Finite Simple Groups and the O'Nan-Scott Theorem, much detailed information concerning primitive permutation groups has now been obtained. While primitive permutation groups are interesting in their own right, primitive permutation groups are actually quite rare, with a ``typical" transitive permutation group being imprimitive. However, primitive permutation groups are the building blocks of imprimitive permutation groups, and so are the building blocks of all transitive groups. We will discuss techniques to analyze imprimitive permutation groups (sometimes using the recently obtained detailed knowledge of primitive permutation groups), with an emphasis on determining information about the automorphism group of a vertex-transitive digraph.