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Theorems · Theorem · group theory

IsOfFinOrder.exists_pow_eq_one

∀ {G : Type u_1} [inst : Monoid G] {x : G}, IsOfFinOrder x → ∃ n, 0 < n ∧ x ^ n = 1

Alias of the forward direction of isOfFinOrder_iff_pow_eq_one.

Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
4 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
Monoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MonoidHom.isOfFinOrder · cited by 6MonoidHom.isOfFinOrderIsOfFinOrder.eq_one · cited by 2IsOfFinOrder.eq_oneIsMulTorsion.extension_closed · cited by 2IsMulTorsion.extension_cl…IsOfFinOrder.apply · cited by 0IsOfFinOrder.applyIsOfFinOrder.groupPowers · cited by 0IsOfFinOrder.groupPowersMonoid · cited by 3887MonoidIsOfFinOrder · cited by 113IsOfFinOrderisOfFinOrder_iff_pow_eq_one · cited by 27isOfFinOrder_iff_pow_eq_o…IsOfFinOrder.exists_pow_eq_oneCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.