On 24 Aug 2011, at 21:07, Alexander Konovalov wrote: > 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 ] >
Scrolling trough the command line history lead to a typo. Certainly, as just pointed out to me by Stefan, the last two lines in the example meant to be gap> RelatorsOfFpGroup(K); [ F1^2, F2^2, F2*F1*F2*F1*F2*F1*F2*F1 ] Alexander _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
