Theorems · Definition · group theory
SemidirectProduct.mulEquivProd
{N : Type u_1} → {G : Type u_2} → [inst : Group N] → [inst_1 : Group G] → N ⋊[1] G ≃* N × GThe group isomorphism between a semidirect product with respect to the trivial map and the product.
- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 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.
- Equivproof · cited by 8,337
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- MulEquivstatement · cited by 1,142
- MulAutstatement · cited by 158
- SemidirectProductstatement and proof · cited by 69
- SemidirectProduct.equivProdproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- SemidirectProduct.mulEquivProd_applystatement and proof · cited by 0
- SemidirectProduct.mulEquivProd_symm_apply_leftstatement and proof · cited by 0
- SemidirectProduct.mulEquivProd_symm_apply_rightstatement and proof · cited by 0