Theorems · Definition · group theory
Subgroup.focalSubgroupOf
{G : Type u_1} → [inst : Group G] → (H : Subgroup G) → Subgroup ↥HThe focal subgroup considered as a subgroup of H.
Note that focalSubgroup H is always contained in H.
- Defined in
- Mathlib.GroupTheory.Focal
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 68 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.
Cites4
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.subgroupOfproof · cited by 122
- Subgroup.focalSubgroupproof · cited by 9
Cited by12
Results whose statement or proof uses this declaration.
- Subgroup.transferFocalstatement and proof · cited by 5
- Subgroup.map_focalSubgroupOfstatement · cited by 3
- Subgroup.transferFocal_eq_powstatement and proof · cited by 2
- Subgroup.commutator_le_focalSubgroupOfstatement · cited by 1
- Subgroup.focalSubgroupOf_defstatement · cited by 1
- Subgroup.focalSubgroupOf_eq_closurestatement · cited by 1
- Subgroup.focalSubgroupOf.mk'_conj_eqstatement · cited by 1
- Subgroup.focalSubgroupOf.pow_index_surjectivestatement and proof · cited by 1
- Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOfstatement and proof · cited by 1
- Subgroup.ker_transferFocal_inf_eq_focalSubgroupstatement · cited by 1
- Subgroup.transferFocal_surjectivestatement and proof · cited by 0
- Subgroup.transferFocal.quotientKerMulEquivQuotientFocalSubroupOfstatement · cited by 0