Theorems · Theorem · group theory
Group.conjugates_subset_normal
∀ {G : Type u_1} [inst : Group G] {N : Subgroup G} [tn : N.Normal] {a : G}, a ∈ N → conjugatesOf a ⊆ ↑N- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.Normal.conj_memproof · cited by 23
- isConj_iffproof · cited by 16
- conjugatesOfstatement and proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Group.conjugatesOfSet_subsetproof · cited by 1