Theorems · Theorem · group theory
Equiv.Perm.sign_mul
∀ {α : Type u} [inst : DecidableEq α] [inst_1 : Fintype α] (f g : Equiv.Perm α),
Equiv.Perm.sign (f * g) = Equiv.Perm.sign f * Equiv.Perm.sign g- Defined in
- Mathlib.GroupTheory.Perm.Sign
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 78 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.
Cites7
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
- Unitsstatement · cited by 2,804
- Equiv.Permstatement and proof · cited by 1,375
- map_mulproof · cited by 1,137
- Equiv.Perm.signstatement and proof · cited by 138
Cited by18
Results whose statement or proof uses this declaration.
- Matrix.det_mulproof · cited by 51
- AlternatingMap.map_permproof · cited by 6
- alternatingGroup.isMultiplyPretransitiveproof · cited by 4
- Matrix.detp_eq_of_row_eqproof · cited by 3
- Equiv.Perm.sign_sumCongrproof · cited by 3
- Equiv.Perm.decomposeFin.symm_signproof · cited by 2
- Equiv.Perm.sign_eq_prod_prod_Iioproof · cited by 2
- Equiv.Perm.sign_of_cycleType'proof · cited by 2
- alternatingGroup.center_eq_botproof · cited by 2
- alternatingGroup.stabilizer.surjective_toPermproof · cited by 2
- alternatingGroup.stabilizer_ne_topproof · cited by 1
- alternatingGroup.exists_mem_stabilizer_smul_eqproof · cited by 1