Theorems · Theorem · group theory
Equiv.Perm.closure_isSwap
∀ {α : Type u} [inst : DecidableEq α] [Finite α], Subgroup.closure {σ | σ.IsSwap} = ⊤- Defined in
- Mathlib.GroupTheory.Perm.Sign
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Set.ofPredstatement · cited by 6,101
- Subgroupstatement · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Equiv.Permstatement · cited by 1,375
- Subgroup.closurestatement · cited by 196
- Equiv.Perm.IsSwapstatement · cited by 35
- Equiv.Perm.mclosure_isSwapproof · cited by 2
- Subgroup.closure_eq_top_of_mclosure_eq_topproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.eq_alternatingGroup_of_index_eq_twoproof · cited by 1
- Equiv.Perm.closure_cycle_adjacent_swapproof · cited by 1
- Equiv.Perm.closure_isCycleproof · cited by 0