Introduction

Abstract algebra

Defining groups

Subgroups

Abelian groups

Group order

Creating groups

Permutations and the symmetric group

Morphisms

Generating sets

Group operations

The group commutator

The direct product of groups

Specifc groups

The trivial group

The infinite cyclic group (\(Z\))

The finite cyclic groups (\(C_n\) or \(Z_n\))

The circle group (\(T\))

Normal subgroups

Cosets and normal subgroups

Quotient groups

Group extension

Theorems

Cayley's theorem

Lagrange's theorem

Group action

Group action