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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).

    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
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