Theorems · Definition · group theory
SemidirectProduct.equivProd
{N : Type u_1} → {G : Type u_2} → [inst : Group N] → [inst_1 : Group G] → {φ : G →* MulAut N} → N ⋊[φ] G ≃ N × GThe bijection between the semidirect product and the product.
- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- MulAutstatement and proof · cited by 158
- SemidirectProductstatement and proof · cited by 69
- SemidirectProduct.rightproof · cited by 35
- SemidirectProduct.leftproof · cited by 30
Cited by5
Results whose statement or proof uses this declaration.
- SemidirectProduct.mulEquivProdproof · cited by 3
- SemidirectProduct.cardproof · cited by 0
- SemidirectProduct.equivProd_applystatement and proof · cited by 0
- SemidirectProduct.equivProd_symm_apply_leftstatement and proof · cited by 0
- SemidirectProduct.equivProd_symm_apply_rightstatement and proof · cited by 0