Introduction to Abstract Group Theory

This course will introduce abstract groups. We will start with definitions, basic properties and constructions and cover many important theorems in basic group theory, such as Lagrange’s theorem, Cauchy’s theorem and Sylow theorems. A major emphasis of the course will be to present numerous worked-out examples and problems. A part of the lecture every week will be devoted to explicit calculations.INTENDED AUDIENCE:BSc, MSc students studying mathematicsPREREQUISITES: Any BSc student who is familiar with high school mathematics can take this courseINDUSTRY SUPPORT: NIL

Syllabus

Week 1: Motivation, definition, examples and basic properties
Week 2: Subgroups, subgroups of integers, homomorphisms
Week 3:Quotient groups, isomorphism theorems
Week 4: Group operations, counting formula
Week 5: Symmetric groups
Week 6: Operations of a group on itself, class equation
Week 7: Sylow theorems I
Week 8: Sylow theorems II