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Math Help - [SOLVED] isomorphisms of groups

  1. #1
    danielap
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    [SOLVED] isomorphisms of groups

    Please, is it possible for somebody to help me with this:

    1). Are (Z, +) and (Q,+) isomorphic?
    2). Are Q, +) and (Q*, *) isomorphic?
    Q* = nonzero rationals

    3). Any finitely generated subgroup of (Q, +, 0) is cyclic.

    How do we do such kind of exercices? Do I need to find a counterexample?
    Those are problems from Nathan Jacobson - Basic Algebra Vol. I.
    There are somewhere on the web some old homeworks from this book?

    I don't know how to post a message for everybody to see it...
    Thank you.
    Dana.
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  2. #2
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    Quote Originally Posted by danielap View Post
    1). Are (Z, +) and (Q,+) isomorphic?
    One iis cyclic and the other is not.

    2). Are Q, +) and (Q*, *) isomorphic?
    Q* = nonzero rationals[/I]
    No. This

    [I]3). Any finitely generated subgroup of (Q, +, 0) is cyclic.
    Is S = \{ 1, 1/2\} cyclic when generated?
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