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Nessary and sufficient condition for homomorphism to be isomorphism.

  1. Sep 9, 2011 #1
    The necessary and sufficient condition for homomorphisim f of a group G into a group G' with kernel K to be isomorphism of G into G' is that k={e}
    .... THOUGH I AM ABLE TO PROVE THAT f IS ONE-ONE AND f IS HOMOMORPHISM (in converse part) BUT CAN'T GET ANY IDEA TO PROVE THAT f IS ONTO.
    PLEASE HELP ME IN THIS REGARD
     
  2. jcsd
  3. Sep 9, 2011 #2

    micromass

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    That Ker(f)={e} is a necessary and sufficient condition for f to be injective.
    You won't be able to prove that f is an isomorphism, because it is false in general.
     
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