in which we apply group theory to prove Fermat-Euler, and use Lagrange to help us find subgroups or determine what a small group must look like.
in which we finish the proof of Lagrange’s Theorem, see what consequences it has on orders of elements, and meet equivalence relations.
in which we show that the sign of a permutation is a surjective group homomorphism, and meet cosets.
in which we prove that disjoint cycle notation works and get a first glimpse of the sign of a permutation.
in which we meet the symmetric groups and their cycle notation.
in which we investigate cyclic groups, generators, dihedral groups and cartesian products of groups.
in which we learn more about group homomorphisms and meet images and kernels.