Dear Taleea Jalaeeyan, > On 20 Nov 2016, at 12:42, taleea jalaeeyan <jalaee...@gmail.com> wrote: > > Thank you gap for answering me. > 1- how can i define commutators of wight more than 3 to gap?
There is an undocumented function `LeftNormedComm`, so [x, y, y, y] is [[[x, y], y], y] > 2- is the concept of Quadratic Non Residue (mod p) is defined for gap? Yes - see `Legendre`, http://www.gap-system.org/Manuals/doc/ref/chap15.html#X81464ABF7F10E544 > how can i define it for a presentation of a group? You will have to construct a group below for some fixed given n and p. For example, gap> Legendre(3,5); -1 so 3 is a quadratic non-residue modulo 5. Now > how can i define the following presentation in gap > \langle x, y |x^{p^{2}}=y^{p}=1, [x, y, x]=1, [x, y, > y]=x^{np}, [x, y, y, y]=1 \rangle > when n is quadratic non residue (mod p)? gap> x:=f.1; x gap> y:=f.2; y gap> n:=3;p:=5; 3 5 gap> rels:=[ > x^(p^2), y^(p), > LeftNormedComm([x,y,x]), > LeftNormedComm([x,y,y])*x^(-n*p), > LeftNormedComm([x,y,y,y]) ]; [ x^25, y^5, y^-1*x^-1*y*x^-1*y^-1*x*y*x, y^-1*x^-1*y*x*y^-1*x^-1*y^-1*x*y^2*x^-15, y^-2*x^-1*y*x*y*x^-1*y^-1*x*y^-1*x^-1*y*x*y^-1*x^-1*y^-1*x*y^3 ] gap> g:=f/rels; <fp group on the generators [ x, y ]> gap> Size(g); 625 gap> IdGroup(g); [ 625, 10 ] Hope this helps Alexander _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
