Theorems · Theorem · group theory
Equiv.Perm.closure_cycle_adjacent_swap
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] {σ : Equiv.Perm α},
σ.IsCycle → σ.support = Finset.univ → ∀ (x : α), Subgroup.closure {σ, Equiv.swap x (σ x)} = ⊤- Defined in
- Mathlib.GroupTheory.Perm.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 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.
Cites37
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 and proof · cited by 13,712
- Top.topstatement · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Set.ofPredproof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- Finset.univstatement and proof · cited by 3,473
- Equiv.Permstatement and proof · cited by 1,375
- pow_zeroproof · cited by 1,094
- Finset.mem_univproof · cited by 361
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.closure_cycle_coprime_swapproof · cited by 1