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. 2. To get a finitely presented C8, the following should be used: g:=f/[f.1^8]); Please see my related tests below: gap> f := FreeGroup( "a"); gap> g:=f/([f.1^7]); <fp group on the generators [ a ]> gap> Elements(g); [ <identity ...>, a, a^6, a^2, a^5, a^3, a^4 ] gap> StructureDescription(g); "C7" gap> g:=f/([f.1^8]); <fp group on the generators [ a ]> gap> StructureDescription(g); "C8" gap> Elements(g); [ <identity ...>, a, a^2, a^4, a^3, a^-3, a^-2, a^-1 ] > HTH > Dima Yours, Hongyi _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
