On Sat, Apr 30, 2022 at 5:19 PM Dima Pasechnik <d...@sagemath.org> wrote: > > On Sat, Apr 30, 2022 at 05:04:57PM +0800, Hongyi Zhao wrote: > > On Sat, Apr 30, 2022 at 4:49 PM Dima Pasechnik <d...@sagemath.org> wrote: > > > > > > On Sat, Apr 30, 2022 at 11:27:37AM +0800, Hongyi Zhao wrote: > > > > Hi GAP team, > > > > > > > > I try to construct the C8 from finitely presented group and check its > > > > isomorphism with permutation group with the following steps: > > > > > > > > gap> f := FreeGroup( "a"); > > > > <free group on the generators [ a ]> > > > > > > > > gap> g:=f/[ f.1, f.1^2, f.1^3, f.1^4, f.1^5, f.1^6, f.1^7 ]; > > > > <fp group on the generators [ a ]> > > > > > > > > gap> h:=IsomorphismPermGroup(g); > > > > [ a ] -> [ () ] > > > > > > > > Is there any problem with my operations? > > > > > > It's correct, as your g is a trivial group (as you take the quotient over > > > the whole group f) > > > > > > To get a finitely presented C8, do > > > > > > g:=f/[f.1^7]); > > > > Thank you for pointing this out. I want to add some additional remarks: > > > > 1. There is a missing `(` in your above code. > > rather, an extra ')' - sorry for typo. It's not needed: > > gap> f := FreeGroup( "a"); > <free group on the generators [ a ]> > gap> g:=f/[f.1^7]; > <fp group on the generators [ a ]>
Nice. Thank you for pointing out this tip. > Best, > Dima Yours, Hongyi _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
