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Theorems · Theorem · group theory

orderOf_eq_zero

∀ {G : Type u_1} [inst : Monoid G] {x : G}, ¬IsOfFinOrder x → orderOf x = 0
Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
5 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Monoid
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Around this declaration

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

orderOf_eq_zero_iff · cited by 8orderOf_eq_zero_iffzpow_pow_orderOf · cited by 2zpow_pow_orderOfNat.card_submonoidPowers · cited by 1Nat.card_submonoidPowersNat.Coprime.orderOf_pow · cited by 1Coprime.orderOf_powRightCancelMonoid.Nat.card_submonoidPowers · cited by 0Nat.card_submonoidPowersMonoid · cited by 3887MonoidorderOf · cited by 324orderOfIsOfFinOrder · cited by 113IsOfFinOrderorderOf_eq_zeroCITED BYCITES

Cites3

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Cited by5

Results whose statement or proof uses this declaration.