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Semi Direct Product

  1. Feb 2, 2008 #1
    thnx for helping on the previous post.

    heres the next one, as usual any hints on how to approach the question would be greatly appreciated. i will attempt the questions with the hints :)

    (1)
    describe explicitly all homomorphisms

    [itex]\varphi : C_4 \rightarrow Aut(C_5)[/itex]

    (2)
    For each such homomorphism [itex]\varphi[/itex] describe the semidirect product [itex]C_5 \rtimes_{\varphi} C_4[/itex] in terms of generators and relations.

    (3) How many distinct isomorphism types of groups of the form [itex]C_5 \rtimes_{\varphi} C_4[/itex] are there?
     
  2. jcsd
  3. Feb 3, 2008 #2

    morphism

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    It will help to know what Aut(C_5) is. Hint: It's cyclic.
     
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