Theorems · Theorem · group theory
Equiv.Perm.IsThreeCycle.mem_alternatingGroup
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {f : Equiv.Perm α}, f.IsThreeCycle → f ∈ alternatingGroup α- Cited by
- 5 results in Mathlib
- Foundations
- Depth 103 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.
Cites7
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
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- alternatingGroupstatement · cited by 96
- Equiv.Perm.IsThreeCyclestatement and proof · cited by 34
- Equiv.Perm.mem_alternatingGroupproof · cited by 7
- Equiv.Perm.IsThreeCycle.signproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.closure_three_cycles_eq_alternatingproof · cited by 3
- Equiv.Perm.isThreeCycle_subset_alternatingGroupproof · cited by 1
- alternatingGroup.subgroup_eq_top_of_isPreprimitiveproof · cited by 1
- Equiv.Perm.IsThreeCycle.alternating_normalClosurestatement · cited by 0
- Equiv.Perm.alternatingGroup_le_of_isPreprimitiveproof · cited by 0