Theorems · Theorem · group theory
Equiv.Perm.mem_alternatingGroup
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {f : Equiv.Perm α},
f ∈ alternatingGroup α ↔ Equiv.Perm.sign f = 1- Cited by
- 7 results in Mathlib
- Foundations
- Depth 79 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.signstatement · cited by 138
- alternatingGroupstatement · cited by 96
- MonoidHom.mem_kerproof · cited by 22
Cited by7
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.mem_alternatingGroupproof · cited by 5
- alternatingGroup.isConj_ofproof · cited by 1
- alternatingGroup.mem_kleinFour_of_order_two_powproof · cited by 1
- Equiv.Perm.prod_list_swap_mem_alternatingGroup_iff_even_lengthproof · cited by 1
- Equiv.Perm.centralizer_le_alternating_iffproof · cited by 0
- alternatingGroup.isConj_swap_mul_swap_of_cycleType_twoproof · cited by 0
- alternatingGroup.normalClosure_swap_mul_swap_fivestatement · cited by 0