[GAP Forum] Construct the C8 from finitely presented group and check its isomorphism with permutation group.

[Hongyi Zhao]

On Sat, Apr 30, 2022 at 5:26 PM Dima Pasechnik <dima at sagemath.org> wrote:
>
> On Sat, Apr 30, 2022 at 05:13:41PM +0800, Hongyi Zhao wrote:
>
> [...]
> > > > 2. Why does the IsomorphismPermGroup(g) give the following result?
> > > >
> > > > [ (1,2,4,6,8,7,5,3) ]
> > >
> > > This means that replacing a with this permutation gives you an insomorphic permutation group.
> >
> > Could you please explain this in more detail? Here we only have one
> > element, i.e., a, so, how to replace it?
>
> The elements of a finitely presented group are words in generators.
> In general, to set up a group homomorphism, it suffices to describe images of group generators.
> (just as for vector spaces, it suffices to describe images of a basis)
>
> One seldom needs to explicitly list all the group elementsi, in general.

Thank you for the clarification.

> HTH
> Dima

Yours,
Hongyi