Theorems · Theorem · group theory
MonoidHom.surjective_of_card_ker_le_div
∀ {G : Type u_1} {M : Type u_2} [inst : Group G] [inst_1 : Group M] [Finite G] [Finite M] (f : G →* M),
Nat.card ↥f.ker ≤ Nat.card G / Nat.card M → Function.Surjective ⇑f- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setproof · cited by 53,352
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- Set.ncardproof · cited by 344
- MonoidHom.rangeproof · cited by 314
- Set.subset_univproof · cited by 228
Cited by2
Results whose statement or proof uses this declaration.
- MonoidHom.domRestrict_surjectiveproof · cited by 2
- FiniteField.unitsMap_norm_surjectiveproof · cited by 1