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Theorems · Inductive type · group theory

AddSubgroup.Characteristic

{A : Type u_4} → [inst : AddGroup A] → AddSubgroup A → Prop

An AddSubgroup is characteristic if it is fixed by all automorphisms. Several equivalent conditions are provided by lemmas of the form Characteristic.iff...

Defined in
Mathlib.Algebra.Group.Subgroup.Basic
Cited by
17 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddSubgroup.characteristic_iff_comap_eq · cited by 4AddSubgroup.characteristi…AddSubgroup.upperCentralSeriesAux · cited by 4AddSubgroup.upperCentralS…AddSubgroup.upperCentralSeries_one · cited by 4AddSubgroup.upperCentralS…AddAut.characteristic · cited by 2AddAut.characteristicAddSubgroup.Characteristic.fixed · cited by 1Characteristic.fixedAddSubgroup.characteristic_iff_comap_le · cited by 1AddSubgroup.characteristi…AddSubgroup.characteristic_iff_le_comap · cited by 1AddSubgroup.characteristi…AddSubgroup.characteristic_iff_map_eq · cited by 1AddSubgroup.characteristi…AddSubgroup.Characteristic.casesOn · cited by 0Characteristic.casesOnAddSubgroup.Characteristic.comap_quotient_mk · cited by 0Characteristic.comap_quot…AddSubgroup.upperCentralSeries.eq_def · cited by 0upperCentralSeries.eq_defAddSubgroup.Characteristic.recOn · cited by 0Characteristic.recOnAddSubgroup.characteristic_biInf · cited by 0AddSubgroup.characteristi…AddSubgroup.characteristic_biSup · cited by 0AddSubgroup.characteristi…AddAut.characteristic_apply_apply_coe · cited by 0AddAut.characteristic_app…AddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddSubgroup.CharacteristicCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.