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Math Help - isomorphic

  1. #1
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    isomorphic

    Let G=\mathbb{Z}_4\times\mathbb{Z}_3. Show that G is isomorphic to \mathbb{Z}_{12}.
    Last edited by Chris L T521; November 21st 2009 at 09:44 PM. Reason: TeXified question
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  2. #2
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    Take (1,1)\in \mathbb{Z}_4 \times \mathbb{Z}_3 then let k\in \mathbb{N} and we have (k1,k1)=0 iff 4\vert k and 3\vert k the least such number is [4,3] (the min. comm. mult.) and it's well known that [a,b](a,b)=ab then since (4,3)=1...
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  3. #3
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    One to one and onto

    The map
    Z12 -> G
    defined by n -> (n mod 4, n mod 3 ) is 1:1 and onto.

    Alternatively,
    G-> Z12
    defined by
    (a,b) -> 3*a + 4*b mod 12
    should also be 1:1 and onto.
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