Contents
1 GROUP
1.1 Permutations
1.2 Cycle Notation
1.3 Subgroups
1.4 Cosets and Lagrange’s Theorem
1.5 Lagrange’s Theorem
1.6 Normal Subgroups
1.7 Practice Problems
2 GROUP ACTIONS
2.1 Class Equation
2.2 Quotient Groups
2.3 Some Fundamental Properties of Homomorphisms
2.4 Fundamental Isomorphism
2.5 Sylow Theorems
2.6 Integers
2.7 The Fundamental Theorem of Arithmetic
2.8 Euler’s Totient Function
2.9 Practice Problems
3 INTRODUCTION TO RING THEORY
3.1 Properties of Rings
3.2 Fields
3.3 Characteristics of Ring
3.4 Ideal
3.5 Factor/Quotient Rings
3.6 Linear Operators (Transformation)
4 INTRODUCTION TO MODULES
4.1 Submodules
5 FIELD EXTENSIONS
5.1 Practice Problems