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Math Help - Isomorphic problem

  1. #1
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    Isomorphic problem

    The nonzero elements of Z_{3}[i] form an Abelian group of order 8 under multiplication. Is it isomorphic to Z_{8}, Z_{4} \oplus Z_{2}, Z_{2} \oplus Z_{2} \oplus Z_{2}?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    The nonzero elements of Z_{3}[i] form an Abelian group of order 8 under multiplication. Is it isomorphic to Z_{8}, Z_{4} \oplus Z_{2}, Z_{2} \oplus Z_{2} \oplus Z_{2}?
    It is \mathbb{Z}_8.*

    *)A classic result is that the multiplicative group of a finite field must be cyclic. That is the only cyclic group on that list.
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