Theorems · Definition · group theory

MulAction.orbitZPowersEquiv

{α : Type u_3} →
  {β : Type u_4} →
    [inst : Group α] →
      (a : α) →
        [inst_1 : MulAction α β] →
          (b : β) → ↑(MulAction.orbit (↥(Subgroup.zpowers a)) b) ≃ ZMod (Function.minimalPeriod (fun x => a • x) b)

The orbit (a ^ ℤ) • b is a cycle of order minimalPeriod ((•) a) b.

Defined in

Mathlib.Data.ZMod.QuotientGroup

Cited by

4 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulAction