1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

    Good hint. :rolleyes:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Group Theory
  1. Group Theory (Replies: 10)

  2. Group theory (Replies: 3)

  3. Group theory (Replies: 3)

  4. Group theory (Replies: 1)

Loading...