Theorems · Theorem · group theory
IsPGroup.exists_card_eq
∀ {p : ℕ} {G : Type u_1} [inst : Group G] [Fact (Nat.Prime p)] [Finite G], IsPGroup p G → ∃ n, Nat.card G = p ^ nAlias of the forward direction of IsPGroup.iff_card.
- Defined in
- Mathlib.GroupTheory.PGroup
- Cited by
- 5 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by5
Results whose statement or proof uses this declaration.
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- Sylow.exists_subgroup_card_pow_prime_of_le_cardproof · cited by 1
- IsPGroup.le_or_disjoint_of_coprimeproof · cited by 1
- IsPGroup.smul_mul_inv_trivial_or_surjectiveproof · cited by 1
- IsZGroup.of_squarefreeproof · cited by 0