An introduction to permutation groups

Abstract

The main focus of this project is the study of the theory of Finite Permutations Groups. Special emphasis will be given to the case of transitive permutation groups, from the basics to Frobenius and Mathieu Group. The long-term goal of the project is two-fold. On the one hand, the student shall learn the tools necessary to use permutation groups in current research problems; for instance, automorphism groups of algebraic curves. On the other hand, the student will use his computational background to try and develop algorithms to study some particular classes of finite permutation groups. The first part of the project shall be based on the study of the classical books on the matter, mainly "Finite Permutation Groups" (H. Wielandt) and "Permutation Groups" (J. D. Dixon, B. Mortimer). Building on this, the student shall later study research papers on the matter, such as "Finite permutation groups and finite simple groups", by Peter J. Cameron.