Category

Theorems about finite groups

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Lagrange's theorem

the theorem that, for a finite group of order a mutiple of 𝑝ⁿ, there exist Sylow 𝑝-subgroups of order 𝑝ⁿ (all of whom are conjugate), whose number equals the index of the normalizer of any such subgroup

Cayley's theorem

theorem in group theory

Cauchy's theorem

Feit–Thompson theorem

theorem that every finite group of odd order is solvable

Burnside's theorem

a result in group theory that is often useful in taking account of symmetry when counting mathematical objects

Brauer–Suzuki theorem

theorem that a finite group with a generalized quaternion Sylow 2-subgroup and no non-trivial normal subgroups of odd order has a center of order 2