Abstract algebra

Defining groups

Subgroups

Abelian groups

Group order

Permutations and the symmetric group

Morphisms

Generating sets

The group commutator

The direct product of groups

The trivial group

The infinite cyclic group (\(Z\))

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

The circle group (\(T\))

Cosets and normal subgroups

Quotient groups

Group extension

Cayley's theorem

Lagrange's theorem

Group action