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External direct products of cyclic groups

  • Thread starter lostNfound
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  • #1
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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?
 

Answers and Replies

  • #2
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The group you posted IS cyclic.
 
  • #3
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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.
 
  • #4
22,097
3,279
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.
It's a product with one factor.
 

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