The usual injection : Z 2 Z 4 is a monomorphism of abelian groups. Show

The usual injection α : Z₂ → Z₄ is a monomorphism of abelian groups. Show that l⊗α :Z₂⊗Z₂ → Z₂⊗Z₄d is the zero map (butZ₂⊗Z₂ ≠ O; see Exercise 2).

Data from exrecise 2

Let A and B be abelian groups.

(a) For each m > 0, A⊗Z_m ≅ A/mA.

(b) Z_m ⊗Zn ≅ Z_c, where c = (m,n).

(c) Describe A⊗B, when A and Bare finitely generated.