Mathlib Map

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 G

If 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.

Cited by3

Results whose statement or proof uses this declaration.