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An Abelian Group Problem

  1. May 28, 2008 #1
    [SOLVED] An Abelian Group Problem

    The problem statement, all variables and given/known data
    Prove: If G is a group where the square of every element equals the identity element, then G is Abelian.

    The attempt at a solution
    I've been able to prove is that a-1 = a and that (ab)-1 = ba where a and b are in G. Everything else I've done leads into a dead-end. Any tips?
     
  2. jcsd
  3. May 28, 2008 #2

    HallsofIvy

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    Okay, you know that a-1= a for every element of the group (including ab) and you know that (ab)-1= ba. What do those two together tell you?
     
  4. May 28, 2008 #3
    I see now! Boy do I feel stupid. Thanks.
     
  5. May 28, 2008 #4

    HallsofIvy

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    Hey, feeling stupid is the beginning of learning!
     
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