HELP:

How many homomorphisms are there from Z20 onto Z8? How many are there to Z8?

Quote:

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How many homomorphisms are there from Z20 onto Z8?

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To map from , you can find out where to

send the generator of .

Since the generator of has order 20, it must be mapped to an

element of order 1, 2, 4, 5, 10, or 20; these are the divisors of 20.

If you want to map them into an element of , then you have to map them to an element of order 1, 2, 4, or 8; these are the possible orders of elements of .