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!

Find all nonisomorphic abelian gps

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data
    - List all nonisomorphic abelian groups of order 2^3 3^2 5


    2. Relevant equations



    3. The attempt at a solution
    - Z_2^3 * Z_3^2 * Z_5 = (iso) Z_360.
    Z_2^3 * Z_3 * Z_3 * Z_5 = (iso) Z_3 * Z_100
    .
    .
    .
    I know ,
    but why Z_360 , Z_3 * Z_100 are nonisomorphic to 2^3 3^2 5 ?
     
  2. jcsd
  3. Apr 16, 2009 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Because Z_360 == Z_2^3 * Z_3^2 * Z_5, but Z_3 * Z_100 == Z_2^3 * Z_3 * Z_3 * Z_5.
     
  4. Apr 16, 2009 #3
    Sorry, I don's understand it..
    Z_2^3 * Z_3 * Z_3* Z_5 == Z_8 * Z_9 * Z_5 Is this nonabelian groups of order
    2^33^25 ??
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook