Title of the course: Permutation groups and combinatorial structure
Instructor: Dr. Zeinab Akhlaghi
Institution: AmirKabir University of Technology (Tehran Polytechnic)
Dates: 4-10 September 2023
Prerequisites: Abstract Algebra, (Definition of groups, normal subgroups, group homomorphisms theorems, group quotient…).
Level: Graduate
Abstract: Permutation groups can be reckoned as the prototype of all groups.
A permutation, in group language, is a bijective function.
A permutation group is a group consisting of permutations on a given set S.
The group of all permutations on S is called the symmetric group of S.
The study of groups arose out of the study of symmetry of geometric objects, which can be interpreted naturally as permutations. We will see that all groups are essentially permutation groups and we will study some properties of permutation groups, like being primitive, faithful, regular and k-transitive.
Language: EN