Conjugacy of elements of finite groups

instance instFintypeConjClasses {α : Type u_1} [Monoid α] [Fintype α] [DecidableRel IsConj] : Fintype (ConjClasses α)

Equations

• instFintypeConjClasses = Quotient.fintype (IsConj.setoid α)

instance instFiniteConjClasses {α : Type u_1} [Monoid α] [Finite α] : Finite (ConjClasses α)

Equations

• (_ : Finite (ConjClasses α)) = (_ : Finite (Quotient (IsConj.setoid α)))

instance instDecidableRelIsConj {α : Type u_1} [Monoid α] [DecidableEq α] [Fintype α] : DecidableRel IsConj

Equations

• instDecidableRelIsConj a b = inferInstanceAs (Decidable (∃ (c : αˣ), ↑c * a = b * ↑c))

instance conjugatesOf.fintype {α : Type u_1} [Monoid α] [Fintype α] [DecidableRel IsConj] {a : α} : Fintype ↑(conjugatesOf a)

Equations

• conjugatesOf.fintype = Subtype.fintype fun (x : α) => x ∈ conjugatesOf a

instance ConjClasses.instFintypeElemCarrier {α : Type u_1} [Monoid α] [Fintype α] [DecidableRel IsConj] {x : ConjClasses α} : Fintype ↑(ConjClasses.carrier x)

Equations

• ConjClasses.instFintypeElemCarrier = Quotient.recOnSubsingleton x fun (x : α) => conjugatesOf.fintype