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!

Proof of union of subgroups as a subgroup

  1. Jul 13, 2008 #1
    Prove that if (H,o) and (K,o) are subgroups of a group (G,o), then (H [tex]\cap[/tex] K,o) is a subgroup of (G,o).

    Proof:
    The identity e of G is in H and K, so e [tex]\in[/tex] H[tex]\cap[/tex]K and H[tex]\cap[/tex]K is not empty. Assume j,k [tex]\in[/tex] H[tex]\cap[/tex]K. Thus jk[tex]^{-1}[/tex] is in H and K, since j and k are in H and K. Therefore, jk[tex]^{-1}[/tex] [tex]\in[/tex] H [tex]\cap[/tex] K making H[tex]\cap[/tex]K a subgroup.

    Just trying to check this proof and see if I did a a good job at it.

    Let (G,o) be an Abelian group and let a,b [tex]\in[/tex] G, Prove that (a o b)[tex]^{2}[/tex]=a[tex]^{2}[/tex] o b[tex]^{2}[/tex]


    Not sure where to begin with this proof. Any help?
     
  2. jcsd
  3. Jul 13, 2008 #2
    Re: Proofs

    The first one is fine
    For the second just use definition of ^2
    (a*b)^2= (a*b)*(a*b)
    and definition of abelian groups i.e cahnging places of elements does not effeect anything
     
  4. Jul 14, 2008 #3
    Re: Proofs

    Thanks for the help matness
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Proof of union of subgroups as a subgroup
Loading...