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Math Help - abstract algebra

  1. #1
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    abstract algebra

    Please help me with my assignment in abstract algebra.

    1. Show that if E is normal in H, then f-1(E) is normal in G.
    2. If G is cyclic, then f(G) is also cyclic.
    Hint: G = <a>. Show: f(G)=< f(a)>.
    3. I G is a cyclic group of infinite order then G is isomorphic to the additive group 2. Hint: f: G→Z by f(a^m) = m.
    Last edited by vldo; November 4th 2010 at 01:13 AM.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by vldo View Post
    Please help me with my assignment in abstract algebra.

    1. Show that if E is normal in H, then f-1(E) is normal in G.
    2. If G is cyclic, then f(G) is also cyclic.
    Hint: G = <a>. Show: f(G)=< f(a)>.
    3. I G is a cyclic group of infinite order then G is isomorphic to the additive group 2. Hint: f: G→Z by f(a^m) = m.
    For 1, What is f-1(E)?

    For 2, I can't really give much more of a hint than the hint given. What have you done so far?

    For 3, you want to find an isomorphism between a group G=<a>, a^n\neq 1 for all n \in \mathbb{N}. What do you think this isomorphism is?
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  3. #3
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    Quote Originally Posted by vldo View Post
    Please help me with my assignment in abstract algebra.

    1. Show that if E is normal in H, then f-1(E) is normal in G.
    2. If G is cyclic, then f(G) is also cyclic.
    Hint: G = <a>. Show: f(G)=< f(a)>.
    3. I G is a cyclic group of infinite order then G is isomorphic to the additive group 2. Hint: f: G→Z by f(a^m) = m.
    Teachers expect questions that form part of an assessment that contributes towards the final grade of a student to be the work of that student and not the work of others. For that reason, MHF policy is to not knowingly help with such questions.

    Thread closed. (You can send me pm to discuss the situation if you want).
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