# 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

Regards,

Raed.

4. Originally Posted by raed
It is the unique coset there is, namely $G=xG\,,\,\,\forall\,x\in G$ .