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!

Centers of groups and products of groups

  1. Oct 30, 2005 #1

    hgj

    User Avatar

    I need to prove that the center of the product of two groups is the product of their centers.

    If I let G and H be two groups, then from definitions, the center of G is Z(G)={z in G such that zg=gz for g in G} and the center of H is Z(H)={z in H sucht that zh=hz for all h in H}. Also, the product of G and H is GxH={(g,h) such that g in G and h in H}. My problem right now is that I'm not sure how to define the center of GxH and I'm not sure how to define the product of Z(G) and Z(H). I'm hoping that if I could understand these two things, I could do the problem.
     
  2. jcsd
  3. Oct 30, 2005 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    GxH is a group. Call it K. Do you know how to define Z(K)?

    Z(G) and Z(H) are groups. Call them P and Q. Do you know how to define PxQ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Centers of groups and products of groups
Loading...