# Math Help - Abstract Algebra Help?

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): $|HK|=\frac{|H||K|}{|H\cap K|}$ ...

Tonio

3. the oder of (H intersect K) can't be greater than the oder of H or the oder of K.
By the Lagerange theorem, the oder of subgroup divides the oder of group.
thus the order of (H intersect K) is a common divisor of the oder of H and the oder of K. since gcd(12,35)=1, that is, the order of (H intersect K) can only be 1.