- Cayley's theorem
- Character orthogonality
- Character table for S₄
- Character table for S₄ using the regular representation
- Class algebra
- Cosets and quotient groups
- Coxeter groups
- Cycle structure of permutation groups and partition of integers
- Derived subgroups
- Dihedral groups
- Direct products of groups
- Definition of a group
- Equivalence classes
- Equivalence (conjugacy) classes of dihedral groups
- Equivalence (conjugacy) classes of permutation groups
- Exponential of a quaternion
- Great orthogonality theorem
- Group of relatively prime numbers
- Group multiplication tables and order-6 groups
- Invariant subgroups
- Invariant symbols and dual tensors
- Irreducible representations of rotation group
- Lemma for relatively prime numbers
- Lie groups, Lie algebras and rotations
- Lie algebra of the rotation group SO(n)
- Permutation groups - cycles and transpositions
- Quaternion arithmetic
- Quaternions as groups
- Real, pseudoreal and complex representations
- Regular representations of groups
- Representations and characters of groups
- Representation of rotation group with rank-2 tensors
- Rotations using quaternions
- Rotations in general using quaternions
- Schur's lemma
- Sets, groups, fields, vector spaces and algebras
- Sizes of irreducible representations
- Square roots of group elements
- Subgroups and Lagrange's theorem
- Test for real, pseudoreal and complex representations
- Two-dimensional representations of the permutation group
- Unitarity theorem for groups
- Vectors as quaternions