Question

How many surjective homomorphisms are there from `ZZ_10` onto `ZZ_5` ?

Answer 1

There are `4`

Explanation:

The (group) homomorphisms from `ZZ_10` onto `ZZ_5` are determined by the value to which `hat(1)` is mapped (since `hat(1)` generates `ZZ_10`). Any of the `4` non-zero members of `ZZ_5` are possible, since they are all of order `5` and generate `ZZ_5`.

So there are `4` possible surjective homomorphisms.