"Source: Text/Group/GrpMatInf.text";
"Line: 1310";
"Date: Thu Apr  1 11:57:57 2021";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatInf.text, line: 1310
// Example: H68E14 ()
print "Example: H68E14";
ei := GetEchoInput();
SetEchoInput(true);
R<s>:= QuadraticField(-1);
F<t>:= FunctionField(R);
M:= MatrixAlgebra (F, 2);
a:= M![-s*t^2 + 1, s*t^3, -s*t, s*t^2 + 1];
b:= M![t^2 - 3*t + 1, 0, 0, t^2 - 3*t + 1];
G:= sub<GL(2,F)|a,b>;
IsNilpotent(G);
assert $1;
IsFinite(G);
assert not $1;
SetEchoInput(ei);
