Still more GroupTheory: Lagrange's Theorem on the size of subgroups. Cosets, normal subgroups and quotient groups. Readings: §20.8.

More detail:

- Cosets of a subgroup; definition, proof that they are all the same size and partition the group (which implies Lagrange's Theorem that the order of a subgroup divides the order of a group).
Applications: no nontrivial proper subgroups for ℤ

_{p}, exactly p+1 nontrivial proper subgroups for D_{p}.- Normal subgroups, congruence modulo a subgroup, and quotient groups.