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Abstract Algebra; Group Theory Question

  1. Mar 11, 2015 #1
    • Member warned about posting without the template and with no effort
    Let N be a normal subgroup of a group G and let f:G→H be a homomorphism of groups such that the restriction of f to N is an isomorphism N≅H. Prove that G≅N×K, where K is the kernel of f.

    I'm having trouble defining a function to prove this. Could anyone give me a start on this?
     
  2. jcsd
  3. Mar 11, 2015 #2

    micromass

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    Start by proving the following:
    1) ##N## and ##K## are normal
    2) ##NK = G##
    3) ##N\cap K = \{e\}##
     
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