Theorems · Definition · group theory
Subgroup.quotientCentralizerEmbedding
{G : Type u_1} → [inst : Group G] → (g : G) → G ⧸ Subgroup.centralizer {g} ↪ ↑(commutatorSet G)Cosets of the centralizer of an element embed into the set of commutators.
- Defined in
- Mathlib.GroupTheory.GroupAction.Quotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Equiv.symmproof · cited by 3,681
- Subgroupstatement · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Function.Embeddingstatement · cited by 988
- Equiv.transproof · cited by 337
- Equiv.toEmbeddingproof · cited by 254
- MulAction.orbitproof · cited by 114
- Function.Embedding.transproof · cited by 83
- ConjActproof · cited by 79
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.quotientCenterEmbeddingproof · cited by 2
- Subgroup.quotientCentralizerEmbedding_applystatement · cited by 0