Theorems · Definition · group theory
Subgroup.orderIsoCon
{G : Type u_1} → [inst : Group G] → { N // N.Normal } ≃o Con GThe normal subgroups correspond to the congruence relations on a group.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 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
- OrderIsostatement · cited by 874
- Subgroup.Normalstatement and proof · cited by 334
- Constatement and proof · cited by 152
- QuotientGroup.conproof · cited by 7
- Con.subgroupproof · cited by 4
- QuotientGroup.con_subgroupproof · cited by 0
Cited by3
Results whose statement or proof uses this declaration.
- QuotientGroup.con_le_iffproof · cited by 1
- Subgroup.orderIsoCon_applystatement and proof · cited by 0
- Subgroup.orderIsoCon_symm_apply_coestatement and proof · cited by 0