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Abstract Algebra: Subgroup Proof

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that if H is a subgroup of G and K is a subgroup of H, then K is a subgroup of G.

    2. Relevant equations

    3. The attempt at a solution
    Well I know that H is a subgroup of G if H is non empty, has multiplication, and his inverses. So I assume that K is a subgroup of H for those same reasons, but I'm unsure how to show K is a subgroup of G based on those two results. I'm looking for the connection. Please help. Thank you.
  2. jcsd
  3. Oct 5, 2011 #2


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    You might be confused because there is not much to show. K is a group in itself. So it has multiplication, inverses and an identity all by itself. I think all you really have to show is that the identity element in K is the same as the identity element in H and G. And, of course, that every element in K is also in H and hence in G. But that's easy.
    Last edited: Oct 6, 2011
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