Groups

Introduction Groups and homomorphisms Groups Homomorphisms Cyclic groups Dihedral groups Direct products of groups Symmetric group I Symmetric groups Sign of permutations Lagrange's Theorem Small groups Left and right cosets Quotient groups Normal subgroups Quotient groups The Isomorphism Theorem Group actions Group acting on sets Orbits and Stabilizers Important actions Applications Symmetric groups II Conjugacy classes in Sn Conjugacy classes in An Quaternions Matrix groups General and special linear groups Actions of GLn(C) Orthogonal groups Rotations and reflections in R2 and R3 Unitary groups More on regular polyhedra Symmetries of the cube Symmetries of the tetrahedron Mobius group Mobius maps Fixed points of Mobius maps Permutation properties of Mobius maps Cross-ratios Projective line (non-examinable)