All Questions

Let $g_1(x,y,z)=(y,x,-z), g_2(x,y,z)=(y,x+y+2z,-y-z)$, $V= \{(x,y,z)\in Z^3|xy-z^2+1=0 \}$. Is it possible to find all orbits of the action of group $\langle g_1 \rangle * \langle g_2 \rangle$ on $V$? ...