Theorems · Theorem · group theory
zpowers_eq_top_of_prime_card
∀ {G : Type u_2} [inst : Group G] {p : ℕ} [hp : Fact (Nat.Prime p)],
Nat.card G = p → ∀ {g : G}, g ≠ 1 → Subgroup.zpowers g = ⊤Any non-identity element of a finite group of prime order generates the group.
- Cited by
- 1 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- Subgroupstatement · cited by 3,593
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardstatement and proof · cited by 844
- Subgroup.zpowersstatement and proof · cited by 204
- Subgroup.eq_bot_or_eq_top_of_prime_cardproof · cited by 3
- Subgroup.zpowers_eq_botproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- mem_zpowers_of_prime_cardproof · cited by 2