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

Marco Costantini costanti at science.unitn.it
Thu Apr 22 11:47:41 BST 2004

```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 ] );