Theorems · Definition · group theory
QuotientGroup.leftRel
{α : Type u_1} → [inst : Group α] → Subgroup α → Setoid αThe equivalence relation corresponding to the partition of a group by left cosets of a subgroup.
- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 66 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.
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
- MulOppositeproof · cited by 1,135
- MulAction.orbitRelproof · cited by 114
- Subgroup.opproof · cited by 58
Cited by65
Results whose statement or proof uses this declaration.
- QuotientGroup.leftRel_applystatement · cited by 17
- QuotientGroup.conproof · cited by 7
- Subgroup.index_comap_of_surjectiveproof · cited by 5
- QuotientGroup.out_eq'statement · cited by 5
- QuotientGroup.out_conj_pow_minimalPeriod_memstatement · cited by 4
- ClassGroup.Quot_mk_eq_mkstatement · cited by 3
- Subgroup.transferFunction_applystatement · cited by 3
- Subgroup.exists_isComplement_leftproof · cited by 3
- Group.nilpotencyClass_quotient_centerproof · cited by 3
- Sylow.fixedPointsMulLeftCosetsEquivQuotientproof · cited by 2
- MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quotstatement · cited by 2
- MulAction.Quotient.mk_smul_outstatement · cited by 2