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Group Theory

  1. Nov 29, 2005 #1
    Hello.

    I was wondering how I could prove if a set of numbers along with some arbitrary operation is an abelian group.
     
  2. jcsd
  3. Nov 30, 2005 #2
    Don't you have a list of axioms which says "G is an abelian group if and only if the following are satisfied: ..."?
     
  4. Dec 2, 2005 #3

    JasonRox

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    The first step is proving that it is a group in the first place.

    If it's not a group, than it certainly isn't an abelian group.

    Then after that, look at the definition of what it means for a group to be abelian. Test it. Then you are done.

    Hint: a*b = b*a (where * is the binary operation)
     
  5. Dec 2, 2005 #4
    Sometimes it feels like people just repeat what I write.
     
  6. Dec 2, 2005 #5

    JasonRox

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    You said...

    Don't you have a list of axioms which says "G is an abelian group if and only if the following are satisfied: ..."?

    That's assuming that it is a group, but he hasn't even shown that yet. I'd worry about proving that it is a group before even thinking about what properties the group might have.
     
  7. Dec 2, 2005 #6
    No it isn't. I even used the plural of "axiom" to try to hint at the fact that several things, rather than just commutativity, needed to be checked.
     
  8. Dec 2, 2005 #7

    JasonRox

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    Good hint. :rolleyes:
     
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