Theorems · Theorem · group theory

IsMulTorsion.quotient_iff

∀ {G : Type u_1} {H : Type u_2} [inst : Group G] {N : Subgroup G} [inst_1 : Group H] {f : G →* H},
  Function.Surjective ⇑f → N = f.ker → IsMulTorsion ↥N → (IsMulTorsion H ↔ IsMulTorsion G)

The image of a quotient is torsion iff the group is torsion.

Defined in

Mathlib.GroupTheory.Torsion

Cited by

1 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

GroupGroup