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: Factor group question

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data
    Suppose that G is an Abelian group and H is a subgroup of G. If every element of H is a square and every element of G/H is a square , prove that every element of G is a square.

    2. Relevant equations

    3. The attempt at a solution
    Let a and b be elements of G. The ab=ba since G is an abeleian group. If H is a subgroup of G, then doesn't H share the same opperations with G? If so, since every element of in H is a square, then a^2*b^2 =(aa)(bb)=(bb)(aa) since G is abelian, H should be abelian. Therefore , there is an element in G that is a square
    Last edited: Oct 24, 2007
  2. jcsd
  3. Oct 24, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    If H is a subgroup of G, then indeed the operation on H is the same as that from G. And since G is abelian, so is H. Indeed, there is an element of G that is a square (in fact, any element from G that is in H is a square).
    But the question was to prove that every element of G is a square.

    You didn't use the information about G/H yet. So let a be any element of G. Now you will want to prove that there exists some element b (or you could very suggestively name it [itex]\sqrt{a}[/itex] such that b b = a. How can you do this?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook