Theorems · Theorem · group theory
Subgroup.eq_bot_of_card_eq
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), Nat.card ↥H = 1 → H = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 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.
Cites6
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 and proof · cited by 844
- Nat.card_eq_one_iff_uniqueproof · cited by 15
- Subgroup.eq_bot_of_subsingletonproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.eq_bot_iff_cardproof · cited by 3
- Group.isCyclic_of_coprime_card_range_card_kerproof · cited by 1