Dear all, Suppose F is a finitely presented group, G a finite index subgroup. Often the value of GeneratorsOfGroup(G) is far from minimal. I have 3 questions.
My first very vague/general question is - is it typically beneficial to first reduce the number of generators of G before doing further computations involving G? Second, I have a question about trying to understand GAP's output when using IsomorphismFpGroup. In my case I have a group G, which is a finite index subgroup of a certain finitely presented group with generators "E" and "V". gap> G := GDATA[1870].stab; Group(<194 generators>) gap> GeneratorsOfGroup(G); [ V^-1*E^2*V^-2*E*V*E^-2*V^2*E^-1, (E*V^-1)^4, (E*V^-2*E)^2*V*E^-2*V*(V*E^-1)^2, (V^-1*E)^2*E*V^-2*E*(V*E^-1)^2*E^-1*V^2*E^-1, E*V^-1*(E*V^-2*E)^2*V*E^-2*V*(V*E^-1)^3, ***omitted the rest of the output*** Next, I try to reduce the number of generators of G via IsomorphismFpGroup: gap> f := IsomorphismFpGroup(G); [ <[ [ 1, 1 ] ]|(V*E)^2*(V*E^-1)^2>, <[ [ 2, 1 ] ]|E*V*(E*V^-1)^2*E*V*E^-1>, <[ [ 3, 1 ] ]|(E*V)^3*E*(V^-1*E^-1)^2>, <[ [ 4, 1 ] ]|V*E*V^-1*(E*V)^3*(E^-1*V)^2>, <[ [ 5, 1 ] ]|(V^-1*E*V*E)^2*V*E^-1*V^-1*E^-1*V>, <[ [ 6, 1 ] ]|(V*E*V^-1*E)^2*V*E*V^-1*(E^-1*V)^2>, <[ [ 7, 1 ] ]|V*(E*V^-1)^2*(E*V)^2*E*V^-1*(E^-1*V)^2*E^-1*V^-1>, <[ [ 8, 1 ] ]|V*(E*V^-1)^5*(E^-1*V^-1)^2*E^-1*V>, <[ [ 9, 1 ] ]|V^-1*(E*V)^2*(E*V^-1)^3*E^-1*V^-1*(E^-1*V)^2>, <[ [ 10, 1 ] ]|V*(E*V^-1)^2*(E*V^-1*E*V)^2*(E^-1*V^-1)^2*E^-1*V> ] -> [ F1, F2, F3, F4, F5, F6, F7, F8, F9, F10 ] What are these "[1, 1]", "[2, 1]" that are appearing? They continue to appear even if I access the corresponding element: gap> finv := InverseGeneralMapping(f);; gap> Image(f).1^finv; <[ [ 1, 1 ] ]|(V*E)^2*(V*E^-1)^2> gap> After reading the GAP manual they seem to have something to do with "straight line program elements", but I still don't know how to interpret them. What is the meaning of [a,b]? My third and final question is - is it possible to update the attribute "GeneratorsOfGroup" for an existing group? For example, I'd like to make it so that the group "G" above uses the 10 generators obtained via IsomorphismFpGroup as opposed to the default "194 generators". Thanks, - Will -- William Chen Member, School of Mathematics Institute for Advanced Study Princeton, NJ, 08540 oxei...@gmail.com _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
