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ENHANCE: FittingFreeLiftSetup (#5510)
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Use cachedFFS to build new map if applicable.
Store new FFHoms in Pool
Reduce generator number of subgroups, also in maxsub code.
Better preimage under ffhom for fitting free.
(Otherwise use orbits first to see whether kernel elements are required, before
calculating orders.)
Avoid trivial images slowing down setup for permhom
Avoid hom on trivial subgroup w/o parent
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@hulpke
hulpke authored Sep 29, 2023
1 parent 7ee7ce9 commit 7d29977
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Showing 5 changed files with 104 additions and 38 deletions.
44 changes: 29 additions & 15 deletions lib/fitfree.gi
View file
Original file line number Diff line number Diff line change
Expand Up @@ -149,9 +149,10 @@ local ffs,pcisom,rest,kpc,k,x,ker,r,pool,i,xx,pregens,iso;
r:=Concatenation(k!.depthsInParent,[Length(ffs.pcgs)+1]);
fi;

AddNaturalHomomorphismsPool(U,ker,rest);
r:=rec(parentffs:=ffs,
rest:=rest,
ker:=ker,
radical:=ker,
pcgs:=k,
serdepths:=List(ffs.depths,y->First([1..Length(r)],x->r[x]>=y))
);
Expand Down Expand Up @@ -183,7 +184,7 @@ local ffs,cache,rest,ker,k,r;
r:=[1..Length(k)];
r:=rec(parentffs:=ffs,
rest:=rest,
ker:=ker,
radical:=ker,
pcgs:=k,
serdepths:=List(ffs.depths,y->First([1..Length(r)],x->r[x]>=y))
);
Expand All @@ -204,7 +205,7 @@ local ffs,cache,rest,ker,k,r;
end);

InstallGlobalFunction(SubgroupByFittingFreeData,function(G,gens,imgs,ipcgs)
local ffs,hom,U,rest,ker,r,p,l,i,depths,pcisom;
local ffs,hom,U,rest,ker,r,p,l,i,depths,pcisom,subsz,pcimgs;

ffs:=FittingFreeLiftSetup(G);
# get back to initial group -- dont induce of induce
Expand Down Expand Up @@ -251,7 +252,21 @@ local ffs,hom,U,rest,ker,r,p,l,i,depths,pcisom;
SetIndicesEANormalSteps(ipcgs,l);
fi;

U:=SubgroupNC(G,Concatenation(gens,ipcgs));
pcimgs:=List(ipcgs,x->ImagesRepresentative(ffs.pcisom,x));

ker:=SubgroupNC(G,List(MinimalGeneratingSet(Group(pcimgs,One(Range(ffs.pcisom)))),
x->PreImagesRepresentative(ffs.pcisom,x)));
SetPcgs(ker,ipcgs);
if Length(ipcgs)=0 then
SetSize(ker,1);
else
SetPcgs(ker,ipcgs);
SetSize(ker,Product(RelativeOrders(ipcgs)));
fi;
subsz:=Size(Group(imgs,One(Image(ffs.factorhom))))*Size(ker);

U:=SubgroupNC(G,Concatenation(gens,GeneratorsOfGroup(ker)));
SetSize(U,subsz);

gens:=Concatenation(gens,ipcgs);
imgs:=Concatenation(imgs,List(ipcgs,x->One(Range(hom))));
Expand All @@ -269,16 +284,8 @@ local ffs,hom,U,rest,ker,r,p,l,i,depths,pcisom;
SetRecogDecompinfoHomomorphism(rest,RecogDecompinfoHomomorphism(hom));
fi;

ker:=SubgroupNC(G,ipcgs);
if Length(ipcgs)=0 then
SetSize(ker,1);
else
SetPcgs(ker,ipcgs);
SetSize(ker,Product(RelativeOrders(ipcgs)));
fi;
SetKernelOfMultiplicativeGeneralMapping(rest,ker);

SetSize(U,Size(Group(imgs,One(Image(ffs.factorhom))))*Size(ker));

if Length(ipcgs)=0 then
r:=[Length(ffs.pcgs)+1];
Expand All @@ -290,7 +297,7 @@ local ffs,hom,U,rest,ker,r,p,l,i,depths,pcisom;
fi;
r:=rec(parentffs:=ffs,
rest:=rest,
ker:=ker,
radical:=ker,
pcgs:=ipcgs,
serdepths:=List(ffs.depths,y->First([1..Length(r)],x->r[x]>=y))
);
Expand All @@ -302,9 +309,15 @@ local ffs,hom,U,rest,ker,r,p,l,i,depths,pcisom;
if ipcgs=MappingGeneratorsImages(ffs.pcisom)[1] then
pcisom:=ffs.pcisom;
else
pcisom:=List(ipcgs,x->ImagesRepresentative(ffs.pcisom,x));
pcisom:=pcimgs;
if Length(ipcgs)>0 then
# work around error for special trivial group.
r:=Group(ipcgs,OneOfPcgs(ipcgs));
else
r:=SubgroupNC(G,ipcgs);
fi;
RUN_IN_GGMBI:=true;
pcisom:=GroupHomomorphismByImagesNC(Group(ipcgs,OneOfPcgs(ipcgs)),
pcisom:=GroupHomomorphismByImagesNC(r,
SubgroupNC(Range(ffs.pcisom),pcisom),
ipcgs,pcisom);
RUN_IN_GGMBI:=false;
Expand All @@ -317,6 +330,7 @@ local ffs,hom,U,rest,ker,r,p,l,i,depths,pcisom;
factorhom:=rest
);
SetFittingFreeLiftSetup(U,r);
AddNaturalHomomorphismsPool(U,ker,rest);
fi;

return U;
Expand Down
44 changes: 37 additions & 7 deletions lib/ghomperm.gi
View file
Original file line number Diff line number Diff line change
Expand Up @@ -18,23 +18,47 @@ InstallMethod( PreImagesSet,
CollFamRangeEqFamElms,
[ IsPermGroupHomomorphism, IsGroup ],
function( map, elms )
local genpreimages, pre,kg,sz;
local genpreimages, pre,kg,sz,ol,orb,pos,dom,one;
genpreimages:=GeneratorsOfMagmaWithInverses( elms );
if Length(genpreimages)>0 and CanEasilyCompareElements(genpreimages[1]) then
# remove identities
genpreimages:=Filtered(genpreimages,i->i<>One(i));
fi;

genpreimages:= List(genpreimages,
gen -> PreImagesRepresentative( map, gen ) );
if fail in genpreimages then
TryNextMethod();
fi;

if HasFittingFreeLiftSetup(Source(map)) and
IsIdenticalObj(map,FittingFreeLiftSetup(Source(map)).factorhom) then
dom:=FittingFreeLiftSetup(Source(map));
pre:=SubgroupByFittingFreeData(Source(map),genpreimages,
GeneratorsOfMagmaWithInverses(elms),dom.pcgs);
return pre;
fi;

if Length(genpreimages)>0 and CanEasilyCompareElements(genpreimages[1]) then
# remove identities
genpreimages:=Filtered(genpreimages,i->i<>One(i));
fi;

one:=One(Source(map));
if HasSize( elms ) then
sz:=Size( KernelOfMultiplicativeGeneralMapping( map ) ) * Size( elms );
kg:=GeneratorsOfGroup(KernelOfMultiplicativeGeneralMapping( map ) );
if Length(kg)>2 then Add(genpreimages,Random(kg));fi;
ol:=Concatenation(genpreimages,kg);
dom:=MovedPoints(ol);
ol:=Length(Orbits(Group(ol,one),dom));
pre:=SubgroupNC(Source(map),genpreimages);
orb:=List(Orbits(pre,dom),Set);
pos:=0;
while Length(orb)>ol do
repeat
pos:=pos+1;
until ForAny(orb,x->OnSets(x,kg[pos])<>x);
Add(genpreimages,kg[pos]);
pre:=SubgroupNC(Source(map),genpreimages);
orb:=List(Orbits(pre,dom),Set);
od;

StabChainOptions(pre).limit:=sz;
while Size(pre)<sz do
pre:=ClosureSubgroupNC(pre,First(kg,i->not i in pre));
Expand Down Expand Up @@ -664,6 +688,7 @@ BindGlobal("DoSCMPermGpHom",function(arg)
dict,
short,
FillTransversalShort,
ntran, # positions of non-identity generators
BuildOrb,
AddToStbO,
maxstor,
Expand Down Expand Up @@ -901,12 +926,16 @@ BindGlobal("DoSCMPermGpHom",function(arg)
size := Length( S.orbit );

# create new elements until we have reached the size

ntran:=Filtered([1..Length(mapi[1])],x->not IsOne(mapi[1][x]));
# catch all trivial case
if Length(ntran)=0 then ntran:=[1..Length(mapi[1])];fi;
while size <> gsize do

# try random elements
elm := rnd[rni];
img := rne[rni];
i := Random( 1, Length( mapi[1] ) );
i := Random(ntran);
rnd[rni] := rnd[rni] * mapi[1][i];
rne[rni] := rne[rni] * mapi[2][i];
rni := rni mod two + 1;
Expand Down Expand Up @@ -1443,6 +1472,7 @@ InstallMethod( CoKernelOfMultiplicativeGeneralMapping, true,
[ IsPermGroupGeneralMappingByImages and
IsToPermGroupGeneralMappingByImages ], 0,
function( hom )
Size(Source(hom)); Size(Range(hom)); # force sizes for RSS
StabChainPermGroupToPermGroupGeneralMappingByImages( hom );
return CoKernelOfMultiplicativeGeneralMapping( hom );
end );
Expand Down
7 changes: 3 additions & 4 deletions lib/grp.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -1255,8 +1255,7 @@ DeclareAttribute( "ConjugacyClasses", IsGroup );
## <Example><![CDATA[
## gap> ConjugacyClassesMaximalSubgroups(g);
## [ Group( [ (2,4,3), (1,4)(2,3), (1,3)(2,4) ] )^G,
## Group( [ (3,4), (1,4)(2,3), (1,3)(2,4) ] )^G,
## Group( [ (3,4), (2,4,3) ] )^G ]
## Group( [ (3,4), (1,3)(2,4) ] )^G, Group( [ (3,4), (2,4,3) ] )^G ]
## ]]></Example>
## </Description>
## </ManSection>
Expand Down Expand Up @@ -1302,8 +1301,8 @@ DeclareAttribute( "MaximalSubgroups", IsGroup );
## of <A>G</A>.
## <Example><![CDATA[
## gap> MaximalSubgroupClassReps(g);
## [ Group([ (2,4,3), (1,4)(2,3), (1,3)(2,4) ]), Group([ (3,4), (1,4)
## (2,3), (1,3)(2,4) ]), Group([ (3,4), (2,4,3) ]) ]
## [ Group([ (2,4,3), (1,4)(2,3), (1,3)(2,4) ]),
## Group([ (3,4), (1,3)(2,4) ]), Group([ (3,4), (2,4,3) ]) ]
## ]]></Example>
## </Description>
## </ManSection>
Expand Down
18 changes: 7 additions & 11 deletions lib/maxsub.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -69,15 +69,6 @@ function( G, fampcgs,pcgs,fphom,words,wordgens,wordimgs)
group := G,
factorfphom:=fphom
);
# giving generators enforces a bad presentation
#generators := GeneratorsOfGroup( G ) );

#for gen in
# List(GeneratorsOfGroup(Range(fphom)),x->PreImagesRepresentative(fphom,x)) do
# gen:=(List(pcgs,y->ExponentsOfPcElement(pcgs,y^gen)));
# Print(gen,"\n");
#od;
#Error("EH");

OCOneCocycles( ocr, false );
if not IsBound( ocr.complement ) then return []; fi;
Expand Down Expand Up @@ -189,6 +180,11 @@ BindGlobal("MaximalSubgroupClassesSol",function(G)
f:=ff.factorhom;
mgi:=MappingGeneratorsImages(ff.factorhom);
sel:=Filtered([1..Length(mgi[2])],x->not IsOne(mgi[2][x]));
if 4^Length(sel)>Size(Range(ff.factorhom)) then
f:=SmallGeneratingSet(Image(ff.factorhom));
mgi:=[List(f,x->PreImagesRepresentative(ff.factorhom,x)),f];
sel:=[1..Length(mgi[1])];
fi;
gensG:=mgi[1]{sel};

# fp group and word representation for gensG
Expand Down Expand Up @@ -903,7 +899,7 @@ local G,types,ff,maxes,lmax,q,d,dorb,dorbt,i,dorbc,dorba,dn,act,comb,smax,soc,
# eliminate those containing the socle
lmax:=Filtered(lmax,x->not IsSubset(x,soc));
Info(InfoLattice,1,Length(lmax)," type 2 maxes");
for mm in lmax do mm!.type:="2";od;
for mm in lmax do mm!.type:="2";od;
Append(maxes,lmax);
fi;

Expand All @@ -913,7 +909,7 @@ for mm in lmax do mm!.type:="2";od;
lmax:=MaxesType3(act[1],Image(act[2],q),act[3],act[4],act[5],true);
Info(InfoLattice,1,Length(lmax)," type 3b maxes");
lmax:=List(lmax,x->PreImage(act[2],x));
for mm in lmax do mm!.type:="3b";od;
for mm in lmax do mm!.type:="3b";od;
Append(maxes,lmax);
fi;

Expand Down
29 changes: 28 additions & 1 deletion lib/permdeco.gi
View file
Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,34 @@ local pcgs,r,hom,A,iso,p,i,depths,ords,b,mo,pc,limit,good,new,start,np;
if Size(r)=1 then
hom:=IdentityMapping(G);
else
hom:=NaturalHomomorphismByNormalSubgroup(G,r);
hom:=fail;
if IsBound(G!.cachedFFS) then
A:=First(G!.cachedFFS,x->IsSubset(x[1]!.radical,r));
if A<>fail then
hom:=A[2].rest;
pcgs:=A[2].pcgs;
pc:=CreateIsomorphicPcGroup(pcgs,true,false);
iso := GroupHomomorphismByImagesNC( r, pc, pcgs, GeneratorsOfGroup( pc ));
r:=rec(inducedfrom:=A[1],
radical:=r,
factorhom:=hom,
depths:=Set(A[2].serdepths), #Set as factors might vanish
pcisom:=iso,
pcgs:=pcgs);
return r;
fi;
A:=First(G!.cachedFFS,x->IsSubset(r,x[1]!.radical));
if A<>fail then
b:=Image(A[2].rest);
b:=NaturalHomomorphismByNormalSubgroupNC(b,RadicalGroup(b));
hom:=A[2]!.rest*b;
SetKernelOfMultiplicativeGeneralMapping(hom,r);
AddNaturalHomomorphismsPool(G,r,hom);
fi;
fi;
if hom=fail then
hom:=NaturalHomomorphismByNormalSubgroup(G,r);
fi;
fi;

A:=Image(hom);
Expand Down

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