[GAP Forum] p-quotient of an infinite matrix group

[Marco Costantini]

Dear gap-forum, 
let G be an infinite matrix group, like in the example below. I'd like to 
study a p-quotient (or a nilpotent-, solvable-, polycyclic- quotient) of 
G (I mean a quotient of the form G / PCentralSeries(G,7)[n]). 
 
The obstacles are that the quotient methods requires a finitely presented 
group, and the conversion from matrix groups to finitely presented groups 
is available only for finite groups. 
 
Are there any suggestion? 
 
r := 
[ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], 
  [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], 
  [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], 
  [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ] ]; 
s := 
[ [ 1, 0, 0, 0, 0, 0, 0, 1 ], [ 0, E(7)^6, 0, 0, 0, 0, 0, 0 ], 
  [ 0, 0, E(7), 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], 
  [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], 
  [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ]; 
 
G:=Group( [ r, s ] ); 
 
Thank you for your attention, 
Marco Costantini