Dear Zeinab, dear Forum, On 20 Apr 2011, at 05:10, zeinab foruzanfar wrote:
> Dear Gap > I am a question? > Let we have SmallGroup(order,n),how we can show finite group of > SmallGroup(order,n) in the form of > <x,y|x^n=y^m=1 ,y^(-1) xy=x^r> > For example finite group of SmallGroup(70,2). > Thanks for your attention You may convert it to the finitely presented group and then use RelatorsOfFpGroup: gap> G:=SmallGroup(70,2); <pc group of size 70 with 3 generators> gap> H:=Image(IsomorphismFpGroup(G)); <fp group of size 70 on the generators [ F1, F2, F3 ]> gap> RelatorsOfFpGroup(H); [ F1^2, F2^-1*F1^-1*F2*F1, F3^-1*F1^-1*F3*F1*F3^-5, F2^5, F3^-1*F2^-1*F3*F2, F3^7 ] Note also the usage of SimplifiedFpGroup which tries to simplify its argument via Tietze transformations. gap> G:=SmallGroup(8,3); <pc group of size 8 with 3 generators> gap> H:=Image(IsomorphismFpGroup(G)); <fp group of size 8 on the generators [ F1, F2, F3 ]> gap> RelatorsOfFpGroup(K); [ F2^-1*F1^-1*F2*F1, F1^8, F2^8 ] gap> RelatorsOfFpGroup(H); [ F1^2, F2^-1*F1^-1*F2*F1*F3^-1, F3^-1*F1^-1*F3*F1, F2^2, F3^-1*F2^-1*F3*F2, F3^2 ] gap> K:=SimplifiedFpGroup(H); <fp group on the generators [ F1, F2 ]> gap> RelatorsOfFpGroup(H); [ F1^2, F2^-1*F1^-1*F2*F1*F3^-1, F3^-1*F1^-1*F3*F1, F2^2, F3^-1*F2^-1*F3*F2, F3^2 ] Hope this helps, Alexander _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
