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Homework Help: Abstract algebra question

  1. Jul 22, 2010 #1
    How many groups are there of order 7.

    I just need to know this to continue with an assignment.

  2. jcsd
  3. Jul 22, 2010 #2
    Take a look at the group elements,

    [tex] Z_{7} = \left\{ 1, a, a^{2},a^{3},a^{4},a^{5},a^{6}\right\}[/tex]
  4. Jul 23, 2010 #3


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    The crucial point is that 7 is a prime number. How many subgroups can a group of order 7 have? What does that tell you?
  5. Jul 23, 2010 #4
    yes in hindsight this was such a duh answer.

    it is one correct?
  6. Jul 23, 2010 #5
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