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!

Proof check: find adirect product representation for Q8 grou

  1. Oct 15, 2015 #1
    1. The problem statement, all variables and given/known data
    Find a direct product representation for the quaternion group. Which are your options?

    2. Relevant equations


    3. The attempt at a solution
    Theorem: The internal direct product of normal subgroups forms a homomorphism of the group.

    https://proofwiki.org/wiki/Internal_Group_Direct_Product_of_Normal_Subgroups

    The quaternion group as 6 normal subgroups, 4 of which are proper.

    Lets suppose I only choose proper subgroups. The orders of these are 2,4,4,4.

    Then I can form the product (grouporder2)x(anyothergrouporder4) and assure myself that it is a isomorphism.

    Therefore, I've created a direct product representation.

    Is this correct?
     
  2. jcsd
  3. Oct 15, 2015 #2
    Note that the intersection of my subgroups is has 2 elements, therefore I think the theorem doesn't apply.

    Also, I'm having doubts as to why any direct product representation of a group has to be made via subgroups. How can I prove this?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Proof check: find adirect product representation for Q8 grou
  1. Product Proof (Replies: 1)

Loading...