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External direct products of cyclic groups

  1. Nov 18, 2011 #1
    I'm wondering if anyone can help me with learning how to write groups as an external direct product of cyclic groups.

    The example I'm looking at is for the subset {1, -1, i, -i} of complex numbers which is a group under complex multiplication. How do I express it as an external direct product of cyclic groups?
     
  2. jcsd
  3. Nov 18, 2011 #2

    micromass

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    The group you posted IS cyclic.
     
  4. Nov 18, 2011 #3
    Right. I understand that the subset of complex numbers shown is a group under multiplication, and I know that it itself is cyclic with i and -i both being generators, but I know it isn't expressed as an external direct product of cyclic groups.
     
  5. Nov 18, 2011 #4

    micromass

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    It's a product with one factor.
     
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