Theorems · Theorem · group theory
IsPGroup.nontrivial_iff_card
∀ {p : ℕ} {G : Type u_1} [inst : Group G],
IsPGroup p G → ∀ [hp : Fact (Nat.Prime p)] [Finite G], Nontrivial G ↔ ∃ n > 0, Nat.card G = p ^ n- Defined in
- Mathlib.GroupTheory.PGroup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Finitestatement and proof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nontrivialstatement and proof · cited by 2,416
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- pow_zeroproof · cited by 1,094
- Nat.cardstatement and proof · cited by 844
- ne_of_gtproof · cited by 637
- Fact.outproof · cited by 328
- Nat.Prime.one_ltproof · cited by 118
- IsPGroupstatement and proof · cited by 96
Cited by2
Results whose statement or proof uses this declaration.
- IsPGroup.center_nontrivialproof · cited by 2
- IsPGroup.card_center_eq_prime_powproof · cited by 1