Theorems · Theorem · group theory
Equiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eq
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {g : Equiv.Perm α} (a : g.Basis) (x : α),
x ∈ Function.fixedPoints ⇑g ∨ ∃ c, ∃ (_ : x ∈ (↑c).support), ∃ m, (g ^ m) (a c) = x- Defined in
- Mathlib.GroupTheory.Perm.Centralizer
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
- Equiv.Perm.SameCycleproof · cited by 116
- Equiv.Perm.cycleFactorsFinsetstatement · cited by 96
- Function.fixedPointsstatement and proof · cited by 90
- Equiv.Perm.cycleOfproof · cited by 59
- Equiv.Perm.mem_supportproof · cited by 51
- Equiv.Perm.Basisstatement and proof · cited by 25
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.Basis.ofPermHomFun_commute_zpow_applyproof · cited by 2
- Equiv.Perm.Basis.ofPermHom_supportproof · cited by 1
- Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iffproof · cited by 1
- Equiv.Perm.Basis.ofPermHomFun_mulproof · cited by 0
- Equiv.Perm.Basis.ofPermHomFun_oneproof · cited by 0