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Cyclic = abelian?

  1. Nov 28, 2005 #1
    is this true for all cases? i know something can be abelian and not cyclic. thanks
     
  2. jcsd
  3. Nov 28, 2005 #2

    TD

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    It's not true, as you say: some can be abelian but not cyclic. So cyclic implies abelian but not necessarily the other way arround.
     
  4. Nov 28, 2005 #3

    matt grime

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    do you perhaps mean implies instead of =?
     
  5. Nov 28, 2005 #4
    yes. other wise my question answers itself. so cyclic implies abelian. thanks for the help.
     
  6. Nov 28, 2005 #5

    matt grime

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    you have proved this (elementary in the sense of asked on the first examples sheet of any course in group theory if at all) result...
     
  7. Dec 1, 2005 #6

    JasonRox

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    I love this property.

    You work with cyclic groups so often that it's so nice to have them all abelian. I love it. :)
     
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