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- 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