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!

Homework Help: Group Theroy problem

  1. Apr 17, 2010 #1
    1. The problem statement, all variables and given/known data
    In Z, let H=<5> and K=<7>. Prove that Z=HK. Is Z the internal direct product of <5> and <7>?

    2. Relevant equations

    3. The attempt at a solution
    Since 3(5)-2(7)=1, every integer n element of Z can be written as 3n(5)+(-2n)(7), and n is an element of HK( where group operation is addition and powers written as multiples). Therefore Z=HK. Since the intersection of H and K =<35>, then Z is not equal to H direct product K.
    I think this is right but I am not sure on some of the justification of my claims. Can any one help me with the justification?
  2. jcsd
  3. Apr 17, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    What part are you finding a hard time justifying? You've shown Z=HK and 5^2*7^2=35*35 so it's not a direct product. What else do you need?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook