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.
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.