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Math Help - Group isomorphism

  1. #1
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    Group isomorphism

    Show  \mathbb{Z}_{14}^* \cong \mathbb{Z}_{18}^* .
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  2. #2
    Super Member PaulRS's Avatar
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    <br />
\mathbb{Z}_{14} ^ \times  <br />
and <br />
\mathbb{Z}_{18} ^ \times  <br />
have the same order and both are cyclic, hence they are isomorphic.

    (Remember that if p>2 is prime then <br />
\mathbb{Z}_{2p^k } ^ \times  <br /> <br />
is cyclic for all k\in \mathbb{Z}^+, to see this, read about primitive roots)
    Last edited by PaulRS; March 10th 2009 at 01:12 PM.
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