/usr/share/gap/grp/ree.gi is in gap-libs 4r7p5-2.
This file is owned by root:root, with mode 0o644.
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#W ree.gi GAP library
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#Y (C) 2001 School Math. Sci., University of St Andrews, Scotland
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#############################################################################
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#M ReeGroupCons( <IsMatrixGroup>, <q> )
##
InstallMethod(ReeGroupCons,"matrix",true,
[IsMatrixGroup,IsPosInt],0,
function ( filter, q )
local theta, m, f, bas, one, zero, x, h, r, gens, G, i;
m:=Int((LogInt(q,3)-1)/2);
if m<0 or q<>3^(1+2*m) then
Error("Usage: ReeGroup(<filter>,3^(1+2m))");
fi;
theta:=3^m;
f:=GF(q);
bas:=BasisVectors(Basis(f));
one:=One(f);
zero:=Zero(f);
x:=function(t,u,v)
return
[[1,t^theta,-u^theta,(t*u)^theta-v^theta,-u-t^(3*theta+1)-(t*v)^theta,
-v-(u*v)^theta-t^(3*theta+2)-t^theta*u^(2*theta),
t^theta*v-u^(theta+1)+t^(4*theta+2)-v^(2*theta)
-t^(3*theta+1)*u^theta-(t*u*v)^theta],
[0,1,t,u^theta+t^(theta+1),
-t^(2*theta+1)-v^theta,-u^(2*theta)+t^(theta+1)*u^theta+t*v^theta,
v+t*u-t^(2*theta+1)*u^theta-(u*v)^theta-t^(3*theta+2)-t^(theta+1)*v^theta],
[0,0,1,t^theta,-t^(2*theta),v^theta+(t*u)^theta,
u+t^(3*theta+1)-(t*v)^theta-t^(2*theta)*u^theta],
[0,0,0,1,t^theta,u^theta,(t*u)^theta-v^theta],
[0,0,0,0,1,-t,u^theta+t^(theta+1)],
[0,0,0,0,0,1,-t^theta],
[0,0,0,0,0,0,1]]*one;
end;
h:=function(t)
return [[t^theta,0,0,0,0,0,0],
[0,t^(1-theta),0,0,0,0,0],
[0,0,t^(2*theta-1),0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,0,0,t^(1-2*theta),0,0],
[0,0,0,0,0,t^(theta-1),0],
[0,0,0,0,0,0,t^(-theta)]]*one;
end;
r:=[[0,0,0,0,0,0,-1],
[0,0,0,0,0,-1,0],
[0,0,0,0,-1,0,0],
[0,0,0,-1,0,0,0],
[0,0,-1,0,0,0,0],
[0,-1,0,0,0,0,0],
[-1,0,0,0,0,0,0]]*one;
# this generating set is not very good -- there is a 2-generator set. AH
gens:=[];
for i in bas do
Add(gens,x(i,zero,zero));
Add(gens,x(zero,i,zero));
Add(gens,x(zero,zero,i));
od;
Add(gens,h(PrimitiveRoot(f)));
Add(gens,r);
G:=Group(gens,One(gens[1]));
SetName(G,Concatenation("Ree(",String(q),")"));
SetDimensionOfMatrixGroup(G,7);
SetFieldOfMatrixGroup(G,f);
SetIsFinite(G,true);
SetSize(G,q^3*(q-1)*(q^3+1));
if q > 3 then SetIsSimpleGroup(G,true); fi;
return G;
end );
PermConstructor(ReeGroupCons,[IsPermGroup,IsObject], IsMatrixGroup);
#############################################################################
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#E ree.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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