1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding subgroups of Factor/ Quotient Groups

  1. Jan 22, 2013 #1
    1. The problem statement, all variables and given/known data

    Describe all the subgroups of Z/9Z. How many are there? Describe all the subgroups of Z/3ZxZ/3Z. How many are there?


    3. The attempt at a solution

    I don't even know where to start with this question. If someone could just point me in the right direction that would be great.

    Thank you.
     
  2. jcsd
  3. Jan 22, 2013 #2
    I have made an attempt, if someone could let me know if it is correct or not, that would be much appreciated!

    The elements of Z/9Z are {0,1,2,3,4,5,6,7,8} with operation modulo9.

    The elements (1,2,4,5,7,8} have order 9 and generate the whole group.
    {0,3,6} has order 3.

    Therefore there are two subgroups.
     
  4. Jan 22, 2013 #3

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    {0} is also a subgroup.
     
  5. Jan 22, 2013 #4
    It looks like you're good for ##Z/9Z##.

    ##Z/3Z \times Z/3Z## is {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)} - which is not cyclic.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding subgroups of Factor/ Quotient Groups
Loading...