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Normal groups

  1. Oct 28, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove by an example, that we can find 3 groups E c F c G, where E is normal in F, F is normal in G, but E is not normal in G.
    (c denotes "contained in")

    Consider:
    G=A_4
    F={Id, (12)(34), (13)(24), (14)(23)} and
    E={Id, (12)(34)}

    3. The attempt at a solution
    I want to use the fact that A_4 is the kernel of S_4 so automatically it is normal in S_4. But how is F related to S_4?
     
  2. jcsd
  3. Oct 30, 2008 #2

    morphism

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    Science Advisor
    Homework Helper

    What do you mean "A_4 is the kernel of S_4"?

    Forget about S_4. Consider the examples you have been given. E is a subgroup of F which in turn is a subgroup of G. Is E normal in F? In G? Is F normal in G?
     
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