# Finitely presented group simplification

Hi! I have a bunch of finitely presented groups, with many generators and relations. I know that all of these are in fact cyclic groups, but many times using the "simplified()" function, I get a simpler presentation with 2 generators, rather than only one. The following is one example:

```
G.<x0,x5> = FreeGroup()
H =G/[(x5^-1*x0)^2*x5^-3, (x0^-1*x5^-1)^2*x0^-2*x5*x0^-1]
```

H is in fact just Z/27Z. Is there another way to simplify these presentations, in order to get a minimal one? The problem here is that I do not only need to identify the specific group, but also to recover the image of the previous generators in the simplified one (as done by the simplification_isomorphism() function).