Theorems · Theorem · group theory
Sylow.iSup_of_normal
∀ {p : ℕ} {G : Type u_1} [inst : Group G] {ι : Type u_2} (H : ι → Subgroup G) [∀ (i : ι), (H i).Normal],
(∀ (i : ι), IsPGroup p ↥(H i)) → IsPGroup p ↥(⨆ i, H i)- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- iSupstatement · cited by 2,415
- Subgroup.Normalstatement and proof · cited by 334
- iSup_leproof · cited by 190
- Classical.arbitraryproof · cited by 161
- Sylowproof · cited by 103
- IsPGroupstatement and proof · cited by 96
- Sylow.isPGroup'proof · cited by 19
- IsPGroup.to_leproof · cited by 5
- IsPGroup.le_sylow_of_normalproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Sylow.biSup_of_normalproof · cited by 1