Theorems · Theorem · group theory
Sylow.smul_subtype
∀ {p : ℕ} {G : Type u_1} [inst : Group G] {P : Sylow p G} {H : Subgroup G} (hP : ↑P ≤ H) (h : ↥H),
h • P.subtype hP = (h • P).subtype ⋯- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites8
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
- Sylowstatement and proof · cited by 103
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.subtypestatement · cited by 10
- Sylow.extproof · cited by 3
- Sylow.smul_lestatement · cited by 2
- Subgroup.conj_smul_subgroupOfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Sylow.conj_eq_normalizer_conj_of_mem_centralizerproof · cited by 1