# Group Theory I & II: Course Outline (MAT 406) For Group Theory I

In mathematics, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups.

## Course Objective

## Course Contents

- Historical background,
- Definition of a group with some examples, Order of an element of a group, Subgroups,
- Generators and relations, Free groups, Cyclic groups, Finite groups,
- Cayley’s theorem on permutation groups,
- Cosets and Lagrange’s theorem,
- Normal subgroups, Simplicity, Normalizers, Direct products, Homomorphism,
- Factor groups, Isomorphism, Automorphism, Isomorphism theorems, Group actions,
- Stabilizers, Conjugacy classes, Sylow theorems and their applications.