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Homework Help: Homomorphism final

  1. Feb 2, 2008 #1
    heres my final one. thnx.

    Show that [itex]A_4[/itex], the group of even permutations on 4 letters, is a semidirect product:
    [itex] A_4 \cong (C_2 \times C_2) \rtimes_{\varphi} C_3 [/itex]

    and describe explicitly the associated homomorphism:
    [itex] \varphi : C_3 \rightarrow Aut(C_2 \times C_2) [/itex]

    thnx for help on the previous posts.
    any help here and ill attempt the rest myself

    kind regards
  2. jcsd
  3. Feb 3, 2008 #2


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    Science Advisor
    Homework Helper

    Have you tried thinking about what A_4 looks like? It's not a very complicated group.
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