Theorems · Theorem · group theory
Sylow.finite_of_finiteIndex
∀ {p : ℕ} {G : Type u_1} [inst : Group G] (P : Sylow p G) [(↑P).FiniteIndex], Finite (Sylow p G)If a Sylow p-subgroup has finite index, then the number of Sylow p-subgroups is finite.
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.FiniteIndex
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupproof · cited by 3,593
- Finitestatement · cited by 3,029
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Sylowstatement and proof · cited by 103
- IsPGroupproof · cited by 96
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.isPGroup'proof · cited by 19
- QuotientGroup.ker_mk'proof · cited by 18
- Subgroup.normalCoreproof · cited by 16
- Subgroup.normalCore_leproof · cited by 10
- IsPGroup.to_leproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Sylow.not_dvd_indexproof · cited by 9