Theorems · Definition · group theory
AddSubgroup.focalAddSubgroupOf
{G : Type u_1} → [inst : AddGroup G] → (H : AddSubgroup G) → AddSubgroup ↥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
- 5 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.focalAddSubgroupproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.map_focalAddSubgroupOfstatement · cited by 2
- AddSubgroup.focalAddSubgroupOf_eq_closurestatement · cited by 1
- AddSubgroup.addCommutator_le_focalAddSubgroupOfstatement · cited by 1
- AddSubgroup.focalAddSubgroupOf_defstatement · cited by 1
- AddSubgroup.focalAddSubgroupOf.mk'_addConj_eqstatement · cited by 0
- AddSubgroup.transferFocalstatement and proof · cited by 0