Theorems · Theorem · group theory
injective_zpow_iff_not_isOfFinOrder
∀ {G : Type u_1} [inst : Group G] {x : G}, (Function.Injective fun n => x ^ n) ↔ ¬IsOfFinOrder x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- pow_zeroproof · cited by 1,094
- zpow_natCastproof · cited by 271
- Int.ModEqproof · cited by 147
- zpow_ofNatproof · cited by 144
- Nat.cast_ne_zeroproof · cited by 113
- IsOfFinOrderstatement and proof · cited by 113
- orderOf_eq_zero_iffproof · cited by 8
- zpow_eq_zpow_iff_modEqproof · cited by 5
- Int.modEq_zero_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.zpowers_eq_zpowers_iffproof · cited by 1