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Homework Help: Homomorphism proof

  1. Dec 12, 2009 #1
    1. The problem statement, all variables and given/known data
    If f:G[tex]\rightarrow[/tex]H is a homomorphism, then f(eG) = eH.

    2. Relevant equations
    The proof from my professor's notes:
    f(eG) = f(eG*GeG) = f(eG)*f(eG)
    f(eG) = f(eG)*eH
    f(eG)*f(eG) = f(eG)*eH
    f(eG) = eH

    3. The attempt at a solutionMy question is, how do you get from the first line to the second. Because it looks like she's using the proposition to prove itself.
  2. jcsd
  3. Dec 12, 2009 #2
    The second line doesn't follow from the first. It simply says that if you multiply any element of H by the identity element of H, you get ... (fill in the rest).

  4. Dec 12, 2009 #3
    :blushing: I feel like an idiot. Thank you!
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