On Sat, Apr 30, 2022 at 11:27 AM Hongyi Zhao <hongyi.z...@gmail.com> 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?
Based on the example given in the GAP - Reference Manual [1], I figured out the following steps: gap> f := FreeGroup( "a"); <free group on the generators [ a ]> gap> g:=f/[ [ f.1^-1, f.1^7] ]; <fp group on the generators [ a ]> gap> Elements( g ); [ <identity ...>, a, a^7, a^2, a^6, a^3, a^5, a^4 ] gap> StructureDescription( g ); "C8" gap> IsomorphismPermGroup(g); [ a ] -> [ (1,2,4,6,8,7,5,3) ] But I still have the following puzzles: 1. Why are the group elements not displayed in the following order? [ <identity ...>, a, a^2, a^3, a^4, a^5, a^6, a^7 ] 2. Why does the IsomorphismPermGroup(g) give the following result? [ (1,2,4,6,8,7,5,3) ] [1] https://www.gap-system.org/Manuals/doc/ref/chap47.html#X7AA982637E90B35A Regards Hongyi _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
