Theorems · Theorem · group theory
AddSubgroup.Normal.conj_mem
∀ {A : Type u_2} [inst : AddGroup A] {H : AddSubgroup A}, H.Normal → ∀ n ∈ H, ∀ (g : A), g + n + -g ∈ HH is closed under additive conjugation
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Normalstatement and proof · cited by 183
Cited by16
Results whose statement or proof uses this declaration.
- AddSubgroup.normalizer_eq_top_iffproof · cited by 6
- AddSubgroup.addCommutator_le_rightproof · cited by 4
- AddSubgroup.Normal.addConj_mem'proof · cited by 4
- AddSubgroup.normal_le_normalCoreproof · cited by 4
- AddSubgroup.upperCentralSeries_monoproof · cited by 3
- AddSubgroup.Normal.comapproof · cited by 2
- AddSubgroup.mem_sup_of_normal_leftproof · cited by 1
- AddSubgroup.mem_sup_of_normal_rightproof · cited by 1
- AddSubgroup.normal_addSubgroupOf_iffproof · cited by 1
- AddSubgroup.Normal.mem_commproof · cited by 1
- AddAction.vadd_orbit_eq_orbit_vaddproof · cited by 1
- AddSubgroup.normal_iInf_normalproof · cited by 1