Theorems · Theorem · group theory
AddSubgroup.map_eq_bot_iff
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (H : AddSubgroup G) {f : G →+ N},
AddSubgroup.map f H = ⊥ ↔ H ≤ f.ker- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubgroup.mapstatement · cited by 189
- AddMonoidHom.kerstatement · cited by 158
- AddSubgroup.gc_map_comapproof · cited by 12
- GaloisConnection.l_eq_botproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- AddGroup.nilpotencyClass_le_of_ker_le_centerproof · cited by 1
- AddSubgroup.comap_eq_kerproof · cited by 1
- AddSubgroup.isNilpotent_of_ker_le_centerproof · cited by 1
- QuotientAddGroup.injective_lift_iffproof · cited by 0
- AddSubgroup.map_ker_selfproof · cited by 0
- AddSubgroup.map_eq_bot_iff_of_injectiveproof · cited by 0