Theorems · Theorem · group theory
IsPGroup.card_orbit
∀ {p : ℕ} {G : Type u_1} [inst : Group G],
IsPGroup p G →
∀ [hp : Fact (Nat.Prime p)] {α : Type u_2} [inst_1 : MulAction G α] (a : α) [Finite ↑(MulAction.orbit G a)],
∃ n, Nat.card ↑(MulAction.orbit G a) = p ^ n- Defined in
- Mathlib.GroupTheory.PGroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Finitestatement and proof · cited by 3,029
- Factstatement and proof · cited by 2,726
- HasQuotient.Quotientproof · cited by 2,301
- Nat.Primestatement and proof · cited by 2,059
- MulActionstatement and proof · cited by 1,294
- Nat.cardstatement · cited by 844
- MulAction.stabilizerproof · cited by 254
- Nat.card_congrproof · cited by 133
- MulAction.orbitstatement and proof · cited by 114
Cited by1
Results whose statement or proof uses this declaration.
- IsPGroup.card_modEq_card_fixedPointsproof · cited by 4