Theorems · Theorem · group theory
Subgroup.map_eq_bot_iff
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (H : Subgroup G) {f : G →* N},
Subgroup.map f H = ⊥ ↔ H ≤ f.ker- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 7 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.
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- MonoidHom.kerstatement · cited by 212
- Subgroup.gc_map_comapproof · cited by 12
- GaloisConnection.l_eq_botproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Group.isSolvable_of_ker_le_rangeproof · cited by 5
- Group.nilpotencyClass_le_of_ker_le_centerproof · cited by 2
- Subgroup.isNilpotent_of_ker_le_centerproof · cited by 2
- QuotientGroup.injective_lift_iffproof · cited by 1
- Subgroup.comap_eq_kerproof · cited by 1
- Subgroup.map_eq_bot_iff_of_injectiveproof · cited by 0
- Subgroup.map_ker_selfproof · cited by 0