# Math Help - Factor Group

1. ## Factor Group

Dear Colleagues,

I have the following question and I need a clear solution to it if possible.

If $G$ is a group what is $G/G$, that is the factor group (coset) of $G$ by $G$.

Regards,

Raed.

2. Originally Posted by raed
Dear Colleagues,

I have the following question and I need a clear solution to it if possible.

If $G$ is a group what is $G/G$, that is the factor group (coset) of $G$ by $G$.

Regards,

Raed.

It is isomorphic with the trivial group with one element, of course.

Tonio

3. Originally Posted by tonio
It is isomorphic with the trivial group with one element, of course.

Tonio
Thank you for your reply. Could you please explain more what is the elements of G/G.

Regards,

Raed.

4. Originally Posted by raed
Thank you for your reply. Could you please explain more what is the elements of G/G.

Regards,

Raed.
It is the unique coset there is, namely $G=xG\,,\,\,\forall\,x\in G$ .

Tonio