Theorems · Theorem · group theory
AddCommMonoid.primaryComponent.disjoint
∀ {G : Type u_1} [inst : AddCommMonoid G] {p : ℕ} [hp : Fact (Nat.Prime p)] {p' : ℕ} [hp' : Fact (Nat.Prime p')],
p ≠ p' → Disjoint (AddCommMonoid.primaryComponent G p) (AddCommMonoid.primaryComponent G p')The p- and q-primary components are disjoint for p ≠ q.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidFactFact
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Factstatement and proof · cited by 2,726
- Disjointstatement · cited by 2,201
- Nat.Primestatement and proof · cited by 2,059
- AddSubmonoidstatement · cited by 1,178
- pow_zeroproof · cited by 1,094
- Fact.outproof · cited by 328
- addOrderOfproof · cited by 208
- Nat.Prime.primeproof · cited by 19
- AddMonoid.addOrderOf_eq_one_iffproof · cited by 6
- eq_of_prime_pow_eqproof · cited by 5
- AddCommMonoid.primaryComponentstatement and proof · cited by 4
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