Theorems · Definition · group theory
QuotientGroup.con
{G : Type u_1} → [inst : Group G] → (N : Subgroup G) → [nN : N.Normal] → Con GThe congruence relation generated by a normal subgroup.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 70 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.
Cites5
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.Normalstatement and proof · cited by 334
- Constatement · cited by 152
- QuotientGroup.leftRelproof · cited by 61
Cited by10
Results whose statement or proof uses this declaration.
- QuotientGroup.liftproof · cited by 8
- Subgroup.orderIsoConproof · cited by 3
- Representation.ofQuotientproof · cited by 3
- QuotientGroup.lift_surjective_of_surjectiveproof · cited by 1
- QuotientGroup.con_le_iffstatement · cited by 1
- QuotientGroup.con_ker_eq_conKerstatement · cited by 0
- Subgroup.orderIsoCon_applystatement · cited by 0
- QuotientGroup.con_monostatement · cited by 0
- QuotientGroup.con_subgroupstatement · cited by 0
- Con.subgroup_quotientGroupConstatement · cited by 0