Theorems · Theorem · group theory
Equiv.Perm.closure_three_cycles_eq_alternating
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α], Subgroup.closure {σ | σ.IsThreeCycle} = alternatingGroup α- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Set.ofPredstatement and proof · cited by 6,101
- Subgroupstatement · cited by 3,593
- mul_assocproof · cited by 1,667
- Equiv.Permstatement and proof · cited by 1,375
- two_mulproof · cited by 232
- Subgroup.closurestatement and proof · cited by 196
- MulMemClass.mul_memproof · cited by 173
- alternatingGroupstatement and proof · cited by 96
- Truncproof · cited by 39
- Equiv.Perm.IsSwapproof · cited by 35
- Equiv.Perm.IsThreeCyclestatement and proof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- commutator_alternatingGroup_eq_topproof · cited by 3
- Equiv.Perm.closure_cycleType_eq_two_two_eq_alternatingGroupproof · cited by 2
- alternatingGroup.closure_isThreeCycles_eq_topproof · cited by 0