1. ## Abstract Algebra Help?

Suppose H and K are subgroups of a group G. If /H/=12 and /K/=35, find /H n K/.

So far I have this:

Let a be an element of H and b an element of K, so then a and b are both elements of G. Then I get stuck.

I am really having trouble with how to work with the orders of H and K in my proof.

2. Originally Posted by mathwiz2006
Suppose H and K are subgroups of a group G. If /H/=12 and /K/=35, find /H n K/.

So far I have this:

Let a be an element of H and b an element of K, so then a and b are both elements of G. Then I get stuck.

I am really having trouble with how to work with the orders of H and K in my proof.

Hint (elephant size): $\displaystyle |HK|=\frac{|H||K|}{|H\cap K|}$ ...

Tonio