Nilo de Roock wrote:
Dear Mike (Newman),Thank you very much for your reply! You wrote that Put H1 = {a,b,c | a^7 = b^13 = a^3 = 1, ab = ba, a^c = a^2, b^c = b^3}., Put H2 = {a,b,c | a^7 = b^13 = a^3 = 1, ab = ba, a^c = a^2, b^c = b^9}. are presentations for the groups of type C91 : C3 and are isomorphic to AllGroups(273)[3] and AllGroups(273)[4] I tried to create these groups to have GAP confirm an isomorphism but until now I failed. For example, for A4, I would do it as follows. ( A4. a^3=1,b^2=1, a*b*a=b*a^-1*b. ) F:=FreeGroup(2);; a:=F.1;; gap> b:=F.2;; H1:=F/[a^3,b^2,a*b*a*b^-1*a*b^-1];; gap> Size(H1); 12 gap> StructureDescription(H1); "A4" gap> List(AllGroups(12),StructureDescription); [ "C3 : C4", "C12", "A4", "D12", "C6 x C2" ] gap> IsomorphismGroups(H1,AllGroups(12)[3]); [ f1, f2 ] -> [ f1*f3, f2*f3 ] And then I get the isomorphism confirmed. Now for H1 = {a,b,c | a^7 = b^13 = a^3 = 1, ab = ba, a^c = a^2, b^c = b^3},
There is a misprint. You have to use c^3 = 1 instead of a^3 = 1.
I tried the same. gap> H1:=F/[a^7,b^13,a^3,a*b*a^-1*b^-1,a^c*a^-2,b^c*b^-3]; <fp group on the generators [ f1, f2, f3 ]> gap> Size(H1); infinity gap> I get a group of inifite order. What am I doing wrong here?? Any hints? Thanks on beforehand for any help.
Hope that helps, Reiner _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
