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    coach32basketball's Avatar
    coach32basketball Posts: 2, Reputation: 1
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    #1

    Jan 9, 2008, 06:37 PM
    Abstract Algebra, don't understand
    HELP:

    How many homomorphisms are there from Z20 onto Z8? How many are there to Z8?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Jan 10, 2008, 02:27 PM
    How many homomorphisms are there from Z20 onto Z8?
    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 .
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