Theorems · Theorem · group theory
AddSubgroup.map_bot
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (f : G →+ N), AddSubgroup.map f ⊥ = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- 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.
Cites7
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 · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubgroup.mapstatement · cited by 189
- GaloisConnection.l_botproof · cited by 63
- AddSubgroup.gc_map_comapproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.isNilpotent_iff_lowerCentralSeriesproof · cited by 2
- AddSubgroup.upperCentralSeries.mapproof · cited by 2
- IsSimpleAddGroup.isSimpleAddGroup_of_surjectiveproof · cited by 1
- AddSubgroup.disjoint_mapproof · cited by 0
- AddSubgroup.lowerCentralSeries_eq_bot_of_nilpotencyClass_leproof · cited by 0
- AddSubgroup.nilpotencyClass_leproof · cited by 0