Theorems · Theorem · group theory
Subgroup.card_eq_one
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, Nat.card ↥H = 1 ↔ H = ⊥- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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
- Subgroupstatement and proof · cited by 3,593
- Nat.cardstatement · cited by 844
- le_bot_iffproof · cited by 116
- Subgroup.relIndex_eq_oneproof · cited by 6
- Subgroup.relIndex_bot_leftproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.disjoint_of_coprime_natCardproof · cited by 3
- NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_oneproof · cited by 2
- IsPGroup.le_or_disjoint_of_coprimeproof · cited by 1
- MonoidHom.ker_transferSylow_disjointproof · cited by 0