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Improved code for NormalSubgroups #376

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Nov 30, 2015
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Improved code for NormalSubgroups #376

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92 changes: 87 additions & 5 deletions lib/grplatt.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -1799,6 +1799,11 @@ local G, # group
still,
ab,
idx,
opr,
zim,
mat,
eig,
qhom,affm,vsb,
T,S,C,A,ji,orb,orbi,cllen,r,o,c,inv,cnt,
ii,i,j,k; # loop

Expand All @@ -1813,6 +1818,7 @@ local G, # group
return InvariantSubgroupsElementaryAbelianGroup(G,[]);
fi;

#cs:=ChiefSeriesTF(G);
cs:=ChiefSeries(G);
G!.lattfpres:=IsomorphismFpGroupByChiefSeriesFactor(G,"x",G);
nt:=[G];
Expand Down Expand Up @@ -1873,11 +1879,87 @@ local G, # group
l:=[];
OCOneCocycles(ocr,true);
if IsBound(ocr.complement) then
l:=BaseSteinitzVectors(BasisVectors(Basis(ocr.oneCocycles)),
BasisVectors(Basis(ocr.oneCoboundaries)));
vs:=VectorSpace(LeftActingDomain(ocr.oneCocycles),
l.factorspace,Zero(ocr.oneCocycles));
Info(InfoLattice,2,p^Length(l.factorspace)," cocycles");
if Length(BasisVectors(Basis(ocr.oneCoboundaries)))>0 then
Error("nontrivial coboundaries basis!");
fi;
vs:=ocr.oneCocycles;
Info(InfoLattice,2,Size(vs)," cocycles");

# get affine action on cocycles that represents conjugation
if Size(vs)>10 then
qhom:=GroupHomomorphismByImagesNC(ocr.group,
Range(ocr.factorfphom),
Concatenation(
MappingGeneratorsImages(ocr.factorfphom)[1],
GeneratorsOfGroup(M)),
Concatenation(
MappingGeneratorsImages(ocr.factorfphom)[2],
List(GeneratorsOfGroup(M),
x->One(Range(ocr.factorfphom)))));
Assert(2,GroupHomomorphismByImages(Source(qhom),Range(qhom),
MappingGeneratorsImages(qhom)[1],
MappingGeneratorsImages(qhom)[2])<>fail);
opr:=function(cyc,elm)
local l,i,lc,lw;
l:=ocr.cocycleToList(cyc);
for i in [1..Length(l)] do
l[i]:=ocr.complementGens[i]*l[i];
od;

# inverse conjugation will give us words that undo the
# action on the factor
lc:=[];
for i in [1..Length(l)] do
lc[i]:=ImagesRepresentative(qhom,l[i]^(elm^-1));
l[i]:=l[i]^elm;
od;
# other generators for same complement, these should be
# nice ones.
lw:=List(lc,x->MappedWord(x,GeneratorsOfGroup(Range(qhom)),l));

lc:=List([1..Length(lc)],x->LeftQuotient(ocr.complementGens[x],lw[x]));
Assert(1,ForAll(lc,x->x in M));

return ocr.listToCocycle(lc);

end;
affm:=[];
vsb:=Basis(vs);
for k in SmallGeneratingSet(G) do
zim:=Coefficients(vsb,opr(Zero(vs),k));
mat:=List(BasisVectors(vsb),x->
Concatenation(Coefficients(vsb,opr(x,k))-zim,[Zero(ocr.field)]));
Add(mat,Concatenation(zim,[One(ocr.field)]));
Add(affm,mat);
od;

# ensure the action is OK
Assert(1,GroupHomomorphismByImages(G,Group(affm),
SmallGeneratingSet(G),affm)<>fail);

#eve:=ExtendedVectors(ocr.field^Length(vsb));
#ooo:=Orbits(Group(affm),eve);
#Info(InfoLattice,2,"orblens=",Collected(List(ooo,Length)));

# common eigenspaces for eigenvalue 1:
eig:=List(affm,x->NullspaceMat(x-x^0));
mat:=eig[1];
for k in [2..Length(eig)] do
mat:=SumIntersectionMat(mat,eig[k])[2];
od;
Info(InfoLattice,2,"eigenspace 1=",Length(mat));
# take only vectors with last entry one
vs:=[];
if Length(mat)>0 then
for k in Elements(VectorSpace(ocr.field,mat)) do
if IsOne(k[Length(k)]) then
Add(vs,k{[1..Length(vsb)]}*vsb);
fi;
od;
fi;
Info(InfoLattice,2,"vectors=",Length(vs));
fi;


# try to catch some solvable cases that look awful
if Size(vs)>1000 and Length(Set(Factors(Index(j,N))))<=2
Expand Down