Theorems · Definition · group theory
AddSubgroup.toSubgroup
{A : Type u_2} → [inst : AddGroup A] → AddSubgroup A ≃o Subgroup (Multiplicative A)Additive subgroups of an additive group A are isomorphic to subgroups of Multiplicative A.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- Subgroupstatement and proof · cited by 3,593
- AddSubgroupstatement and proof · cited by 3,232
- Submonoidproof · cited by 3,086
- AddSubmonoidproof · cited by 1,178
- Multiplicativestatement and proof · cited by 875
- OrderIsostatement · cited by 874
- Additiveproof · cited by 356
- Subgroup.toSubmonoidproof · cited by 114
- AddSubgroup.toAddSubmonoidproof · cited by 91
- Submonoid.toAddSubmonoidproof · cited by 5
Cited by17
Results whose statement or proof uses this declaration.
- Subgroup.toAddSubgroup'proof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroModproof · cited by 2
- zpowersHom_ker_eqproof · cited by 1
- AddSubgroup.fg_iff_mul_fgstatement and proof · cited by 1
- Multiplicative.mem_toSubgroupstatement · cited by 0
- AddMonoidHom.coe_toMultiplicative_mapstatement · cited by 0
- IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eqproof · cited by 0
- AddSubgroup.finiteIndex_toSubgroup_iffstatement · cited by 0
- AddSubgroup.toSubgroup_closurestatement and proof · cited by 0
- AddSubgroup.toSubgroup_comapstatement · cited by 0
- AddSubgroup.coe_toSubgroup_applystatement and proof · cited by 0
- AddSubgroup.coe_toSubgroup_symm_applystatement and proof · cited by 0