The final part introduces maps between groups. Homomorphisms, their kernels and images, the normality criterion, and factor-group construction form a single arc that ends with simple groups — the atoms of group theory.

Sequence

1. Homomorphisms — structure-preserving maps, kernels, and images.
2. Factor Groups — quotient groups from normal subgroups.
3. Factor-Group Computations and Simple Groups — practical computations and groups with no proper nontrivial normal subgroups.