Theorems · Theorem · group theory
GroupExtension.range_inl_eq_ker_rightHom
∀ {N : Type u_1} {E : Type u_2} {G : Type u_3} [inst : Group N] [inst_1 : Group E] [inst_2 : Group G]
(self : GroupExtension N E G), self.inl.range = self.rightHom.kerThe range of the inclusion map is equal to the kernel of the projection map.
- Defined in
- Mathlib.GroupTheory.GroupExtension.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, 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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- MonoidHom.rangestatement · cited by 314
- MonoidHom.kerstatement · cited by 212
- GroupExtensionstatement and proof · cited by 52
- GroupExtension.rightHomstatement · cited by 29
- GroupExtension.inlstatement · cited by 22
Cited by6
Results whose statement or proof uses this declaration.
- GroupExtension.Section.inv_mul_mem_range_inlproof · cited by 1
- GroupExtension.Section.mul_inv_mem_range_inlproof · cited by 1
- GroupExtension.rightHom_inlproof · cited by 1
- GroupExtension.Section.mul_inv_mul_mul_mem_range_inlproof · cited by 1
- GroupExtension.Section.mul_mul_mul_inv_mem_range_inlproof · cited by 1
- GroupExtension.quotientRangeInlEquivRightproof · cited by 0