Theorems · Theorem · group theory
isConj_iff
∀ {α : Type u} [inst : Group α] {a b : α}, IsConj a b ↔ ∃ c, c * a * c⁻¹ = b- Defined in
- Mathlib.Algebra.Group.Conj
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- mul_inv_cancelproof · cited by 128
- inv_mul_cancelproof · cited by 107
- SemiconjByproof · cited by 99
- IsConjstatement and proof · cited by 43
- mul_inv_eq_iff_eq_mulproof · cited by 13
Cited by16
Results whose statement or proof uses this declaration.
- Equiv.Perm.isConj_iff_cycleType_eqproof · cited by 4
- Equiv.Perm.isConj_swapproof · cited by 3
- ConjAct.mem_orbit_conjActproof · cited by 2
- Equiv.Perm.isConj_of_support_equivproof · cited by 2
- card_comm_eq_card_conjClasses_mul_cardproof · cited by 2
- IsArithFrobAt.exists_primesOver_isConjproof · cited by 2
- Equiv.Perm.isConj_of_cycleType_eqproof · cited by 1
- alternatingGroup.isConj_ofproof · cited by 1
- Equiv.Perm.Disjoint.isConj_mulproof · cited by 1
- Group.conjugates_subset_normalproof · cited by 1
- ConjClasses.mk_bijOnproof · cited by 1
- Equiv.Perm.eq_alternatingGroup_of_index_eq_twoproof · cited by 1