Still more GroupTheory: Lagrange's Theorem on the size of subgroups. Cosets, normal subgroups and quotient groups. Readings: §20.8.
- 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 ℤp, exactly p+1 nontrivial proper subgroups for Dp.
- Normal subgroups, congruence modulo a subgroup, and quotient groups.