Theorems · Theorem · group theory
Equiv.Perm.card_compl_support_modEq
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {p n : ℕ} [hp : Fact (Nat.Prime p)] {σ : Equiv.Perm α},
σ ^ p ^ n = 1 → σ.supportᶜ.card ≡ Fintype.card α [MOD p]- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqFact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Compl.complstatement and proof · cited by 2,925
- Factstatement and proof · cited by 2,726
- Finset.cardstatement and proof · cited by 2,327
- Nat.Primestatement and proof · cited by 2,059
- Fintype.cardstatement · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- pow_zeroproof · cited by 1,094
- LT.lt.neproof · cited by 872
- Fact.outproof · cited by 328
- orderOfproof · cited by 324
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.exists_fixed_point_of_prime'proof · cited by 1
- Equiv.Perm.card_fixedPoints_modEqproof · cited by 0
- Equiv.Perm.exists_fixed_point_of_primeproof · cited by 0