Theorems · Theorem · group theory
Subgroup.map_bot
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (f : G →* N), Subgroup.map f ⊥ = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 10 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.
- Groupstatement and proof · cited by 6,238
- Bot.botstatement · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Subgroup.mapstatement · cited by 301
- GaloisConnection.l_botproof · cited by 63
- Subgroup.gc_map_comapproof · cited by 12
Cited by10
Results whose statement or proof uses this declaration.
- Group.isSolvable_of_ker_le_rangeproof · cited by 5
- Subgroup.upperCentralSeries.mapproof · cited by 3
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3
- Subgroup.isNilpotent_iff_lowerCentralSeriesproof · cited by 2
- IsSimpleGroup.isSimpleGroup_of_surjectiveproof · cited by 1
- Group.isSolvable_iff_commutator_ltproof · cited by 1
- Subgroup.nilpotencyClass_leproof · cited by 0
- Subgroup.smul_botproof · cited by 0
- Subgroup.disjoint_mapproof · cited by 0
- Subgroup.lowerCentralSeries_eq_bot_of_nilpotencyClass_leproof · cited by 0