Theorems · Theorem · group theory
orderOf_dvd_sub_iff_zpow_eq_zpow
∀ {G : Type u_1} [inst : Group G] {x : G} {a b : ℤ}, ↑(orderOf x) ∣ a - b ↔ x ^ a = x ^ b- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites5
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
- orderOfstatement · cited by 324
- mul_inv_eq_oneproof · cited by 20
- zpow_subproof · cited by 15
- orderOf_dvd_iff_zpow_eq_oneproof · cited by 2
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