1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Prove a group is abelian

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution

    For the first question, since [f(a)][g(a)] is in C, can I just say that since C is a ring, it is an abelian group, then the four axioms are proven? Then just show closure? Probably not I'm guessing. Associativity of multiplying functions seems so fundamental to me that I really don't know what to do...

    For the second question, shall I start by using composition of functions and then the properties of composition of a function and its inverse, and then go on about the identity function?

    Attached Files:

    Last edited by a moderator: Apr 10, 2013
  2. jcsd
  3. Apr 10, 2013 #2
    I'd say question one is asking you to flesh out the group structure.

    1. What's the identity element? (make sure it's a member of C^A).

    2. For each element f, what's the inverse element? (make sure it's well defined
    - namely, why can you find f^-1 for each f? )

    Closure is trivial but should be mentioned, namely why is (fg) a well
    defined member of C^A when f and g are?

    Associativity (and Abelian-ness) of course follow from the properties of C,
    but you should have a proof showing f(gh) =(fg)h.

    For question 2. I don't know what A-hat is. What do you know
    about group homomorphisms at this point?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted