Title of the course: Introduction to Group Theory
Prof. Ali Nesin
İstanbul Bilgi Ü.
10-30 July 2017
Some familiarity with abstract mathematics
Level: Math majors and graduate students
Abstract: Definition and basic properties. Examples: permutation groups, free groups, direct sums and
direct products. Subgroups and examples. Subgroups generated by subsets. Order of an element. Cosets.
Theorems of Lagrange and Cauchy. Coset spaces, normal subgroups and quotient groups. Homomorphism.
Examples. Kernel. The fundamental theory of group theory and its applications. Group permutations. Sylow theorems.
Language: Depending on the audience English or Turkish