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Homework Help: Cyclic Subgroup of Z30

  1. Sep 7, 2010 #1
    1. (a) List all elements in H=<9>, viewed as a cyclic subgroup of Z30
    (b) Find all z in H such that H=<z>





    I'm thinking that H=<9> = {1,7,9} (viewed as a cyclic subgroup of Z30) is this correct?
    And could someone explain what (b) is asking in other terms?
     
  2. jcsd
  3. Sep 7, 2010 #2
    No that is not correct. Z30 is an additive group so H=<9> contains 9, 9+9, 9+9+9 etc.

    Part (b) asks which elements of H could produce H by just adding it to itself repeatedly
     
  4. Sep 7, 2010 #3
    so {9,18,27}?
     
  5. Sep 7, 2010 #4
    No, quite a few more. What do you get if you add 9 to 27 in Z30?
     
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