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Showing isomorphism?

  1. Oct 7, 2008 #1

    tgt

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    What would be the technique to show A is isomorphic to (B intersection C)?


    where A, B and C are groups.
     
  2. jcsd
  3. Oct 7, 2008 #2

    HallsofIvy

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    The obvious way: construct an iosomorphism from A to (B intersection C).

    Of course, how you construct such an isomorphism will depend on exactly what A, B, and C are, since whether they are isomorphic depends on what they are!

    That is, find a function that assigns, to every member of A, a specific member of B intersect C and then show that it:
    1) preserves the operation: f(x*y)= f(x)*f(y)
    2) maps the indentity in A to the identity in B.
    3) is one-to-one.
    4) maps A "onto" B intersect C.
     
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