Algebra I

Groups, dihedral groups, symmetric groups, quaternion groups, homomorphisms, isomorphisms, group actions, subgroups, centralizers, normalizers, stabilizers, kernels, cyclic groups, lattices, quotient groups, cosets, Lagrange's theorem, isomorphism theorems, composition series, Alternating groups, permutation representations, Cayley’s theorem, the class equation, automorphisms, Sylow theorems, simplicity of alternating group, direct products, finitely generated abelian groups, small order groups, semidirect products, nilpotent groups, solvable groups, p-groups, medium order groups, free groups.