Theorems · Definition · group theory
Subgroup.quotientCenterEmbedding
{G : Type u_1} →
[inst : Group G] → {S : Set G} → Subgroup.closure S = ⊤ → G ⧸ Subgroup.center G ↪ ↑S → ↑(commutatorSet G)If G is generated by S, then the quotient by the center embeds into S-indexed sequences
of commutators.
- Defined in
- Mathlib.GroupTheory.GroupAction.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Function.Embeddingstatement · cited by 988
- Equiv.toEmbeddingproof · cited by 254
- Subgroup.closurestatement and proof · cited by 196
- Subgroup.centerstatement · cited by 121
- Function.Embedding.transproof · cited by 83
- Subgroup.centralizerproof · cited by 65
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.index_center_le_powproof · cited by 1
- Subgroup.quotientCenterEmbedding_applystatement · cited by 0