## Lecture Notes

### Group Theory

Much part of these lecture notes came from Modern Algebra (Group Theory) course I taught.

These lecture notes should be accessible by undergraduate students of mathematics or physics who have taken Linear Algebra.

#### Lecture Notes

#### Problem Sets

#### References and Further Reading

Click on linked topics to view lecture notes.

An Overview

Functions

Basic Number Theory

Examples of Groups

Subgroups

Laglange's Theorem

Congruence Modulo \(n\)

Homomorphisms

Normal Subgroups

Quotient Groups

The Isomorphism Theorems

Direct Products

Finitely Generated Abelian Groups

Click on the following links for problems.

Stanley N. Burris and H. P. Shankappanavar, A Course in Universal Algebra, Graduate Texts in Mathematics, Springer-Verlag, 1981

This book is not about group theory but if you are interested in studying general algebra beyond group theory (in the sense of Nicolas Bourbaki?), this is a wonderful book which can be downloaded for free from the website of Stanley N. Burris (linked above).

John B. Fraleigh, A First Course in Abstract Algebra, 7th Edition, Pearson, 2002I. N. Herstein, Abstract Algebra, 3rd Edition, Wiley, 1996

I. N. Herstein, Topics in Algebra, 2nd Edition, John Wiley & Sons, 1975