Theorems · Theorem · group theory
Sylow.not_dvd_index
∀ {p : ℕ} {G : Type u_1} [inst : Group G] [Fact (Nat.Prime p)] (P : Sylow p G) [(↑P).FiniteIndex], ¬p ∣ (↑P).indexA Sylow p-subgroup has index indivisible by p.
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finiteproof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- Subgroup.indexstatement · cited by 150
- Subgroup.FiniteIndexstatement and proof · cited by 113
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Nat.card_posproof · cited by 36
- Sylow.not_dvd_index'proof · cited by 1
- Sylow.finite_of_finiteIndexproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3
- Sylow.pow_dvd_card_of_pow_dvd_cardproof · cited by 2
- Sylow.mapSurjective_surjectiveproof · cited by 2
- Sylow.card_coprime_indexproof · cited by 2
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- Subgroup.focalSubgroupOf.pow_index_surjectiveproof · cited by 1
- Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOfproof · cited by 1
- MonoidHom.not_dvd_card_ker_transferSylowproof · cited by 1
- Sylow.not_dvd_card_commutator_or_not_dvd_index_commutatorproof · cited by 1