Theorems · Definition · group theory

AddGroup.fintypeOfKerLeRange

{F : Type u_1} →
  {G : Type u_2} →
    {H : Type u_3} →
      [inst : AddGroup F] →
        [inst_1 : AddGroup G] →
          [inst_2 : AddGroup H] → [Fintype F] → [Fintype H] → (f : F →+ G) → (g : G →+ H) → g.ker ≤ f.range → Fintype G

If F and H are finite such that ker(G →+ H) ≤ im(F →+ G), then G is finite.

Defined in

Mathlib.GroupTheory.QuotientGroup.Finite

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddGroupAddGroupFintypeFintype