|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file runs a vast number of consistency checks on a large number of
## groups.
SetAssertionLevel(2);
TestsForGroup:=function(G)
local u,cs,ncs,n,rep,i,au,hom,cl,co;
Print("testing group ",G,"\n");
cs:=CompositionSeries(G);
ncs:=List(cs,i->Normalizer(G,i));
Assert(1,ForAll([1..Length(cs)],i->IsNormal(ncs[i],cs[i])));
IsSolvable(G); # enforce the (more instable) solvable algorithms even on
Assert(1,IsNormal(G,Centre(G)));
u:=fail;
if Length(AbelianInvariants(CommutatorFactorGroup(G)))<6 then
if Size(G)<500 then
Print("subgroups\n");
u:=ConjugacyClassesSubgroups(G);
for i in u do
rep:=Subgroup(G,GeneratorsOfGroup(Representative(i)));
Assert(1,Index(G,Normalizer(G,rep))=Size(i));
Assert(1,IsNormal(Normalizer(G,rep),rep));
od;
fi;
if Size(G)<10000 then
Print("normal subgroups\n");
n:=NormalSubgroups(G);
# did we already get them as subgroups?
if u<>fail then
Assert(1,Number(u,i->Size(i)=1)=Length(n));
fi;
for i in n do
Assert(1,IsNormal(G,i));
hom:=NaturalHomomorphismByNormalSubgroup(G,i);
Assert(1,Index(G,i)=Size(Image(hom,G)));
if IsSolvableGroup(i) then
co:=ComplementClassesRepresentatives(G,i);
Assert(1,ForAll(co,j->Size(j)=Index(G,i)
and Size(Intersection(i,j))=1));
if u<>fail then
Assert(1,Length(co)=Number(u,
j->Size(Representative(j))=Index(G,i)
and Size(Intersection(Representative(j),i))=1));
fi;
fi;
od;
fi;
fi;
Assert(1,IsNormal(G,Centre(G)));
Print("conjugacy classes\n");
cl:=ConjugacyClasses(G);
Assert(1,Sum(List(cl,Size))=Size(G));
for i in cl do
Assert(1,Centralizer(i)=Centralizer(G,Representative(i)));
Assert(1,Size(i)=Index(G,Centralizer(i)));
Assert(1,Length(Orbit(Centralizer(i),Representative(i)))=1);
od;
Print("rational classes\n");
cl:=RationalClasses(G);
Assert(1,Sum(List(cl,Size))=Size(G));
if Length(AbelianInvariants(CommutatorFactorGroup(G)))<=3 then
Print("automorphism group\n");
au:=AutomorphismGroup(G);
if HasNiceMonomorphism(au) then
AbelianInvariants(CommutatorFactorGroup(au));
fi;
fi;
end;
ConsistencyChecksForGroups:=function(arg)
local deg,sz,anzdeg,anzsz,i,j;
deg:=2;
sz:=2;
i:=0;
j:=0;
if Length(arg)>0 then
deg:=arg[1];
i:=arg[2];
sz:=arg[3];
j:=arg[4];
fi;
TransGrpLoad(deg,0);
repeat
Print(deg,",",i,",",sz,",",j,"\n");
i:=i+1;
if i>TRANSLENGTHS[deg] then
deg:=deg+1;
TransGrpLoad(deg,0);
i:=1;
fi;
if deg<=TRANSDEGREES then
TestsForGroup(TransitiveGroup(deg,i));
fi;
j:=j+1;
if j>NumberSmallGroups(sz) then
sz:=sz+1;
j:=1;
fi;
if sz<=1000 and not sz in [512,768] then
TestsForGroup(SmallGroup(sz,j));
fi;
until deg>TRANSDEGREES and sz>1000;
Print("passed!\n");
end;
[ Dauer der Verarbeitung: 0.6 Sekunden
(vorverarbeitet)
]
|
