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Homework Help: Isomorphism question

  1. May 31, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove that Z2+Dn and D2n are not isomorphic whenever n is even by using structural characteristics that demonstrate Z2+Dn and D2n cannot be isomorphic.

    2. Relevant equations

    3. The attempt at a solution
    We know that D2n has 2n+1 order 2 elements, since n is even we know that Dn has n+1 elements of order 2. Thus Z2+Dn has 2(n+1)= 2n+2 order 2 elements. Thus Z2+Dn and D2n are not isomorphic whenever n is even. Is this all I need for this question?
  2. jcsd
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