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Group problems

  1. Feb 6, 2008 #1
    1. The problem statement, all variables and given/known data
    Let G be a group and let #G=77. Prove the following:
    a) G is cyclic, if there is such an element a in G that a21≠1 and a22≠1
    b) If there are such elements a and b, so that ord(a)=7 and ord(b)=11, then G=<a,b>

    2. Relevant equations, 3. The attempt at a solution
    I really don't even know where to begin with these. So I'd appreciate if someone could point me in the right direction.
     
  2. jcsd
  3. Feb 6, 2008 #2

    HallsofIvy

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    You do understand, don't you, that any proper subgroups must be of order 7 and 11? And that are subgroups of those orders? That should make (b) trivial.

    As for (a) the crucial point is that 21= 3*7 and 22= 2*11.
     
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