Thread: Isomorphism Question

G has 16 elements and H has 4 elements....so G/H = 4?

Now I have what seems like a corollary in my book, but not stated as...it says "a group of order 4 is isomorphic to Z4 or Z2+Z2 (direct prodcut)"...so would the first part be yes? Maybe I am over complicating things...
and then on the second part
k = <(1,2)>
How do you find out how many elements a generating function like K has?

Originally Posted by xyz

G has 16 elements and H has 4 elements....so G/H = 4?

Now I have what seems like a corollary in my book, but not stated as...it says "a group of order 4 is isomorphic to Z4 or Z2+Z2 (direct prodcut)"...so would the first part be yes? Maybe I am over complicating things...
and then on the second part
k = <(1,2)>
How do you find out how many elements a generating function like K has?

I'm sorry. But do you know what means?

Let G be a group and let H be a normal subgroup of G.
The set G/H = {aH | a ∈ G} is a group under the operation (aH)(bH) = abH. I mentioned that the order of G/H is 4.

what makes and different is that which is not true in now we have so if you let then

because thus such situation does not happen in which means