1. Limited time only! Sign up for a free 30min personal 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!

Mutliplication table of quotient groups

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data
    Write the multiplication table of C[tex]_{6}[/tex]/C[tex]_{3}[/tex]
    and identify it as a familiar group.

    2. Relevant equations

    3. The attempt at a solution
    The cosets are C3 and [tex]\omega^3[/tex]C3
    I just need help making the multiplication table.
  2. jcsd
  3. Nov 23, 2009 #2
    I'm assuming [itex]C_n[/itex] and [itex]C^n[/itex] both refer to the cyclic group of order n, since that's the impression I get from your post.

    if you meant for [itex]C_6[/itex] to be generated by [itex]\omega[/itex], then you should have [itex]C_3 = \{1,\omega^2,\omega^4\}[/itex] because otherwise [itex]C_3[/itex] is not a group. Then the cosets should be [itex]C_3[/itex], [itex]\omega C_3[/itex].

    What exactly are you having trouble with? As you said yourself the group [itex]C_6/C_3[/itex] has exactly two elements ([itex]C_3[/itex] and [itex]\omega C_3[/itex]), so the following four are the possible products you need to compute and insert in the multiplication table:
    [tex]C_3 \times C_3[/tex]
    [tex]C_3 \times \omega C_3[/tex]
    [tex]\omega C_3 \times C_3[/tex]
    [tex]\omega C_3 \times \omega C_3[/tex]
    Last edited: Nov 23, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Mutliplication table of quotient groups
  1. Quotient groups (Replies: 1)

  2. Quotient Groups (Replies: 4)

  3. Quotient groups (Replies: 4)

  4. Quotient Group (Replies: 13)

  5. Quotient group (Replies: 2)