Theorems · Theorem · group theory
Monoid.exponent_pi
∀ {ι : Type u_1} [inst : Fintype ι] {M : ι → Type u_2} [inst_1 : (i : ι) → Monoid (M i)],
Monoid.exponent ((i : ι) → M i) = Finset.univ.lcm fun x => Monoid.exponent (M x)The exponent of finite product of monoids is the Finset.lcm of the exponents of the
constituent monoids.
- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Monoidstatement and proof · cited by 3,887
- Finset.univstatement and proof · cited by 3,473
- Finset.mem_univproof · cited by 361
- Monoid.exponentstatement and proof · cited by 128
- dvd_transproof · cited by 50
- Finset.lcmstatement and proof · cited by 37
- dvd_antisymmproof · cited by 23
- orderOf_dvd_iff_pow_eq_oneproof · cited by 22
- Pi.one_applyproof · cited by 22
- Monoid.order_dvd_exponentproof · cited by 14
- Function.surjective_evalproof · cited by 11
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