Theorems · Theorem · group theory
SemidirectProduct.range_inl_eq_ker_rightHom
∀ {N : Type u_1} {G : Type u_2} [inst : Group N] [inst_1 : Group G] {φ : G →* MulAut N},
SemidirectProduct.inl.range = SemidirectProduct.rightHom.ker- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- le_antisymmproof · cited by 2,068
- MonoidHom.rangestatement · cited by 314
- MonoidHom.kerstatement and proof · cited by 212
- MulAutstatement and proof · cited by 158
- SemidirectProductstatement and proof · cited by 69
- SemidirectProduct.rightproof · cited by 35
- SemidirectProduct.leftproof · cited by 30
- SemidirectProduct.inlstatement and proof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- SemidirectProduct.toGroupExtensionproof · cited by 3
- isZGroup_iff_exists_mulEquivproof · cited by 0