Abstract Algebra: Subgroup Proof

[schmitty10]

Homework Statement

Show that if H is a subgroup of G and K is a subgroup of H, then K is a subgroup of G.

Homework Equations

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.

 

[Dick]

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.