Theorems · Definition · group theory
Sylow.subtype
{p : ℕ} → {G : Type u_1} → [inst : Group G] → (P : Sylow p G) → {N : Subgroup G} → ↑P ≤ N → Sylow p ↥NA sylow subgroup of G is also a sylow subgroup of a subgroup of G.
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.subtypeproof · cited by 185
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.comapOfInjectiveproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- Sylow.coe_subtypestatement · cited by 4
- Sylow.normalizer_sup_eq_top'proof · cited by 2
- Sylow.not_dvd_index'proof · cited by 1
- Sylow.conj_eq_normalizer_conj_of_mem_centralizerproof · cited by 1
- isZGroup_of_coprimeproof · cited by 1
- Sylow.smul_subtypestatement · cited by 1
- Sylow.subtype.congr_simpstatement and proof · cited by 1
- Sylow.subtype_injectivestatement and proof · cited by 1
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- Sylow.normalizer_normalizerproof · cited by 1