Theorems · Theorem · group theory
AddMonoid.exponent_pi
∀ {ι : Type u_1} [inst : Fintype ι] {M : ι → Type u_2} [inst_1 : (i : ι) → AddMonoid (M i)],
AddMonoid.exponent ((i : ι) → M i) = Finset.univ.lcm fun x => AddMonoid.exponent (M x)The exponent of finite product of additive monoids is the Finset.lcm of the
exponents of the constituent additive monoids.
- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- AddMonoidstatement and proof · cited by 2,864
- Finset.mem_univproof · cited by 361
- Pi.zero_applyproof · cited by 70
- AddMonoid.exponentstatement and proof · cited by 70
- dvd_transproof · cited by 50
- Finset.lcmstatement and proof · cited by 37
- Pi.smul_applyproof · cited by 28
- dvd_antisymmproof · cited by 23
- addOrderOf_dvd_iff_nsmul_eq_zeroproof · cited by 17
- Function.surjective_evalproof · cited by 11
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