Theorems · Theorem · group theory
IsPGroup.to_quotient
∀ {p : ℕ} {G : Type u_1} [inst : Group G], IsPGroup p G → ∀ (H : Subgroup G) [inst_1 : H.Normal], IsPGroup p (G ⧸ H)- Defined in
- Mathlib.GroupTheory.PGroup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 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.
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
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.Normalstatement and proof · cited by 334
- IsPGroupstatement and proof · cited by 96
- QuotientGroup.mk'proof · cited by 90
- Quotient.mk''_surjectiveproof · cited by 19
- IsPGroup.of_surjectiveproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOfproof · cited by 1
- IsPGroup.indexproof · cited by 1
- Subgroup.focalSubgroupOf.pow_index_surjectiveproof · cited by 1
- IsPGroup.isNilpotentproof · cited by 1