Theorems · Theorem · group theory
IsSimpleGroup.isSimpleGroup_of_surjective
∀ {G : Type u_1} [inst : Group G] {H : Type u_3} [inst_1 : Group H] [IsSimpleGroup G] [Nontrivial H] (f : G →* H),
Function.Surjective ⇑f → IsSimpleGroup H- Defined in
- Mathlib.GroupTheory.Subgroup.Simple
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupproof · cited by 3,593
- Nontrivialstatement and proof · cited by 2,416
- Subgroup.Normalproof · cited by 334
- Subgroup.mapproof · cited by 301
- Subgroup.comapproof · cited by 154
- IsSimpleGroupstatement and proof · cited by 26
- Subgroup.comap_topproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- MulEquiv.isSimpleGroupproof · cited by 1