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Homework Help: Need help!

  1. Aug 30, 2010 #1
    got it thanks!
    Last edited: Aug 30, 2010
  2. jcsd
  3. Aug 30, 2010 #2
    homormophism. f(ab)=f(a)f(b) for all a,b in G

    so, imagine the domain and codomain, a will maps to f(a), b will map to f(b), so ab must map to f(ab)
    so it is homorphism if f(ab)=f(a)f(b)
  4. Aug 30, 2010 #3
    so, how does this relate to it being commutative? can we say that f(a)f(b)=f(b)f(a)?
  5. Aug 30, 2010 #4
    that is if and only if proof, so first assume it is homomorphism, so you know f(ab)=f(a)f(b)
    so you want to prove f(a)f(b)=f(b)f(a) or ab=ba, prove either one since both domain and codomain are G

    and conversely, assume that G is commutative, so you know ab=ba or f(a)f(b)=f(b)f(a) chose either one, to prove that f(ab)=f(a)f(b)
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