List of Topics

No. of

Weeks

Introduction and examples:

Definition of a group, subgroups, examples

1-2

Cyclic groups,  generating sets and Caley Diagrams

3-4

Permutations, groups of symmetries (triangle, rectangle, square),   Co-sets, and Direct Products of groups.

5-6

Homomorphisms between groups normal subgroups  and factor groups, automorphisms of groups

7-8

Group Action on a set (Orbit Stabilizer Theorem), fixed points, p-groups, examples

9-11

conjugacy classes, class equations

12-13

Sylow theorems of finite groups

14-15