Theorems · Theorem · group theory
Group.exponent_quotient_dvd
∀ {G : Type u} [inst : Group G] (H : Subgroup G) [inst_1 : H.Normal], Monoid.exponent (G ⧸ H) ∣ Monoid.exponent GIf H is a normal subgroup of G, then the exponent of G ⧸ H divides the exponent of G.
- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.Normalstatement and proof · cited by 334
- Monoid.exponentstatement · cited by 128
- QuotientGroup.mk'_surjectiveproof · cited by 15
- MonoidHom.exponent_dvdproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- CommGroup.card_domRestrictHom_kerproof · cited by 2
- MonoidHom.domRestrict_surjectiveproof · cited by 2
- CommGroup.forall_monoidHom_apply_eq_one_iffproof · cited by 0