# How can you operate in a quotient of a group finitely presented?

Hello everyone, I have the following groups

```
G.<a,b> = FreeGroup()
H = G.quotient([a*b*a.inverse()*b.inverse()])
```

I would like SAGE to understand the product of to lateral clases in H? It is that possible?

Thanks in advance!

What kind of product should be constructed?

We have for instance:

The form

`a^3*b^4*a^-7*b^2`

for the above product computed in H is a possible one. There is no simplification, since there is no "canonical form" to simplify in a general quotient. But the equality`h == H(a^-4 * b^6)`

could be verified.Is there any reason to use

`H`

and not`A`

as above?