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# Group Homomorphism: Hom($Z/105Z,Z/42Z$) and Hom($Z/42Z,Z/105Z$)

ABSALG-884JYS

Let $\mathbb{Z}/m\mathbb{Z}$ be the additive group of integers mod $m\ge 1$. (This group is often denoted $\mathbb{Z}_m$.)

1) There are

group homomorphisms from $\mathbb{Z}/105\mathbb{Z}$ to $\mathbb{Z}/42\mathbb{Z}$.
The set of such homomorphisms forms

group.

2) There are

group homomorphisms from $\mathbb{Z}/42\mathbb{Z}$ to $\mathbb{Z}/105\mathbb{Z}$.
The set of such homomorphisms forms

group.