Theorems · Definition · group theory
Subgroup.toAddSubgroup
{G : Type u_1} → [inst : Group G] → Subgroup G ≃o AddSubgroup (Additive G)Subgroups of a group G are isomorphic to additive subgroups of Additive G.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- Group
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- AddSubgroupstatement and proof · cited by 3,232
- Submonoidproof · cited by 3,086
- AddSubmonoidproof · cited by 1,178
- Multiplicativeproof · cited by 875
- OrderIsostatement · cited by 874
- Additivestatement and proof · cited by 356
- Subgroup.toSubmonoidproof · cited by 114
- AddSubgroup.toAddSubmonoidproof · cited by 91
- Submonoid.toAddSubmonoidproof · cited by 5
Cited by22
Results whose statement or proof uses this declaration.
- Subgroup.strictPeriodsproof · cited by 63
- Subgroup.toAddSubgroup_closurestatement and proof · cited by 3
- Subgroup.mem_strictPeriods_iffproof · cited by 3
- AddSubgroup.toSubgroup'proof · cited by 2
- Subgroup.index_toAddSubgroupstatement · cited by 2
- NumberField.Units.dirichletUnitTheorem.logEmbedding_kerstatement and proof · cited by 2
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- Subgroup.fg_iff_add_fgstatement and proof · cited by 1
- NumberField.Units.regOfFamily_div_regOfFamilyproof · cited by 1
- NumberField.Units.span_basisOfIsMaxRankstatement · cited by 1
- Subgroup.relIndex_toAddSubgroupstatement · cited by 1
- NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsionstatement · cited by 1