"Source: Text/LieTheory/GrpLie.text";
"Line: 470";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/GrpLie.text, line: 470
// Example: H113E2 ()
print "Example: H113E2";
ei := GetEchoInput();
SetEchoInput(true);
q := 5;
k := GF(q);
K := GF(q^2);
G := GroupOfLieType( "A3", K : Isogeny:="SC" );
A := AutomorphismGroup(G);
AGRP := GammaGroup( k, A );
Gamma,m := ActingGroup(AGRP);
Gamma;
m;
action  := GammaAction(AGRP);
time GaloisCohomology(AGRP);
TrivialOneCocycle( AGRP );
c := OneCocycle( AGRP, [GraphAutomorphism(G, Sym(3)!(1,3))] );
x := Random(G);
IsInTwistedForm( x, c );
assert not $1;
x := elt< G | <1,y>, <3,y @ m(Gamma.1)> > where y is Random(K);
IsInTwistedForm( x, c );
assert $1;
SetEchoInput(ei);
