Groups
Cauchy's theorem (group theory)
Sylow theorems
Group action
Burnside's lemma
Centralizer and normalizer
Conjugacy class
Octahedral symmetry
Quaternions and spatial rotation
Finite Fields
Finite field
Finite field arithmetic
Splitting field
Construction of splitting fields
Separable polynomial
Normal extension
Separable extension
Galois extension
Galois theory
Codes
Cyclic code
BCH code
Berlekamp–Massey algorithm
Reed–Solomon error correction