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removed all SubdirectProductWithEmbeddings code #83

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Merged
cdwensley merged 1 commit into from
Aug 13, 2025
Merged

removed all SubdirectProductWithEmbeddings code #83

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10 changes: 0 additions & 10 deletions lib/groups.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -44,16 +44,6 @@ DeclareGlobalName( "ListOfPowers" );
##
DeclareOperation( "GeneratorsAndInverses", [ IsMagmaWithInverses ] );

#############################################################################
## this function has been copied from main library gprd.gd and renamed
##
#O SubdirectProductWithEmbeddings(<G>, <H>, <Ghom>, <Hhom> )
##
DeclareGlobalName( "SubdirectProductWithEmbeddings" );
DeclareOperation( "SubdirectProductWithEmbeddingsOp",
[ IsGroup, IsGroup, IsGroupHomomorphism, IsGroupHomomorphism ] );
DeclareAttribute( "SubdirectProductWithEmbeddingsInfo", IsGroup, "mutable" );

#############################################################################
##
#E groups.gd . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
309 changes: 0 additions & 309 deletions lib/groups.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -105,315 +105,6 @@ InstallMethod( GeneratorsAndInverses, "for groups", true, [ IsGroup ], 0,
G -> Concatenation( GeneratorsOfGroup(G),
List( GeneratorsOfGroup(G), g->g^-1 ) ) );




#############################################################################
## temporary methods for SubdirectProductWithEmbeddings
##
BindGlobal( "SubdirectProductWithEmbeddings",
function(G,H,ghom,hhom)
local iso;
if ( Range( ghom, G ) <> Range( hhom, H ) ) or
( Image( ghom, G ) <> Image( hhom, H ) ) then
Error("the image groups are not the same");
fi;
if not ( IsPermGroup(G) and IsPermGroup(H) ) or
( IsPcGroup(G) and IsPcGroup(H) ) then
Error("methods only supplied forperm groups or pc groups");
fi;
return SubdirectProductWithEmbeddingsOp( G, H, ghom, hhom );
end);

#############################################################################
##
#M SubdirectProductWithEmbeddingsOp( <G>, <H>, <ghom>, <hhom> )
##
InstallMethod( SubdirectProductWithEmbeddingsOp,"groups", true,
[ IsGroup, IsGroup, IsGroupHomomorphism, IsGroupHomomorphism ], 0,
function( G, H, ghom, hhom )
local gc,hc,S,info;
# try to enforce a common representation
if not (IsFinite(G) and IsFinite(H)) then
TryNextMethod();
fi;
if IsSolvableGroup(G) and IsSolvableGroup(H) and
not (IsPcGroup(G) and IsPcGroup(H)) then
# enforce pc groups
gc:=IsomorphismPcGroup(G);
hc:=IsomorphismPcGroup(H);
elif not (IsPermGroup(G) and IsPermGroup(H)) then
# enforce perm groups
gc:=IsomorphismPermGroup(G);
hc:=IsomorphismPermGroup(H);
else
TryNextMethod();
fi;
ghom := InverseGeneralMapping(gc)*ghom;
hhom := InverseGeneralMapping(hc)*hhom;
# the ...Op is installed for `IsGroupHomomorphism'. So we have to enforce
# the filter to be set.
if not IsGroupHomomorphism(ghom) or not IsGroupHomomorphism(hhom) then
Error("mappings are not homomorphisms");
fi;
S:=SubdirectProductWithEmbeddingsOp(Image(gc,G),Image(hc,H),ghom,hhom);
info:=rec(groups:=[G,H],
homomorphisms:=[ghom,hhom],
projections:=[Projection(S,1)*InverseGeneralMapping(gc),
Projection(S,2)*InverseGeneralMapping(hc)]);
S:=Group(GeneratorsOfGroup(S));
SetSubdirectProductWithEmbeddingsInfo(S,info);
return S;
end);

#############################################################################
##
#M Projection( <S>, <i> ) . . . . . . . . . . . . . . . . . make projection
##
InstallMethod( Projection,"pc subdirect product", true,
[ IsGroup and HasSubdirectProductWithEmbeddingsInfo, IsPosInt ], 0,
function( S, i )
local prj, info;
if not i in [1,2] then
Error("only 2 embeddings");
fi;
info := SubdirectProductWithEmbeddingsInfo( S );
if not IsBound(info.projections[i]) then
TryNextMethod();
fi;
return info.projections[i];
end);

#############################################################################
##
#M Size( <S> ) . . . . . . . . . . . . . . . . . . . . of subdirect product
##
InstallMethod( Size,"subdirect product", true,
[ IsGroup and HasSubdirectProductWithEmbeddingsInfo ], 0,
function( S )
local info;
info := SubdirectProductWithEmbeddingsInfo( S );
return Size( info.groups[ 1 ] ) * Size( info.groups[ 2 ] )
/ Size( ImagesSource( info.homomorphisms[ 1 ] ) );
end );

#############################################################################
## methods copied from gprdperm.gi
##
#############################################################################
##
#M SubdirectProductWithEmbeddingsOp( <G1>, <G2>, <phi1>, <phi2> )
##
InstallMethod( SubdirectProductWithEmbeddingsOp, "permgroup", true,
[ IsPermGroup, IsPermGroup, IsGroupHomomorphism, IsGroupHomomorphism ], 0,
function( G1, G2, phi1, phi2 )
local S, # subdirect product of <G1> and <G2>, result
gens, # generators of <S>
D, # direct product of <G1> and <G2>
emb1, emb2, # embeddings of <G1> and <G2> into <D>
info, Dinfo,# info records
gen; # one generator of <G1> or kernel of <phi2>

# make the direct product and the embeddings
D := DirectProduct( G1, G2 );
emb1 := Embedding( D, 1 );
emb2 := Embedding( D, 2 );

# the subdirect product is generated by $(g_1,x_{g_1})$ where $g_1$ loops
# over the generators of $G_1$ and $x_{g_1} \in G_2$ is abitrary such
# that $g_1^{phi_1} = x_{g_1}^{phi_2}$ and by $(1,k_2)$ where $k_2$ loops
# over the generators of the kernel of $phi_2$.
gens := [];
for gen in GeneratorsOfGroup( G1 ) do
Add( gens, gen^emb1 * PreImagesRepresentativeNC(phi2,gen^phi1)^emb2 );
od;
for gen in GeneratorsOfGroup(
KernelOfMultiplicativeGeneralMapping( phi2 ) ) do
Add( gens, gen ^ emb2 );
od;

# and make the subdirect product
S := GroupByGenerators( gens );
SetParent( S, D );

Dinfo := DirectProductInfo( D );
info := rec( groups := [G1, G2],
homomorphisms := [phi1, phi2],
olds := Dinfo.olds,
news := Dinfo.news,
perms := Dinfo.perms,
projections := [] );
SetSubdirectProductWithEmbeddingsInfo( S, info );
return S;
end );

#############################################################################
##
#R IsProjectionSubdirectProductWithEmbeddingsPermGroup( <hom> ) . projection onto factor
##
DeclareRepresentation( "IsProjectionSubdirectProductWithEmbeddingsPermGroup",
IsAttributeStoringRep and IsComponentObjectRep and
IsGroupHomomorphism and IsSurjective and
IsSPGeneralMapping, [ "component" ] );

#############################################################################
##
#M Projection( <S>, <i> ) . . . . . . . . . . . . . . . . . make projection
##
InstallMethod( Projection,"perm subdirect product",true,
[ IsPermGroup and HasSubdirectProductWithEmbeddingsInfo,
IsPosInt ], 0,
function( S, i )
local prj, info;
info := SubdirectProductWithEmbeddingsInfo( S );
if IsBound( info.projections[i] ) then return info.projections[i]; fi;

prj := Objectify( NewType( GeneralMappingsFamily( PermutationsFamily,
PermutationsFamily ),
IsProjectionSubdirectProductWithEmbeddingsPermGroup ),
rec( component := i ) );
SetSource( prj, S );
info.projections[i] := prj;
SetSubdirectProductWithEmbeddingsInfo( S, info );
return prj;
end );

#############################################################################
##
#M Range( <prj> ) . . . . . . . . . . . . . . . . . . . . . . of projection
##
InstallMethod( Range,"perm subdirect product projection",
true, [ IsProjectionSubdirectProductWithEmbeddingsPermGroup ], 0,
prj -> SubdirectProductWithEmbeddingsInfo( Source( prj ) ).groups[ prj!.component ] );

#############################################################################
##
#M ImagesRepresentative( <prj>, <g> ) . . . . . . . . . . . . of projection
##
InstallMethod( ImagesRepresentative,"perm subdirect product projection",
FamSourceEqFamElm,
[ IsProjectionSubdirectProductWithEmbeddingsPermGroup,
IsMultiplicativeElementWithInverse ], 0,
function( prj, g )
local info;
info := SubdirectProductWithEmbeddingsInfo( Source( prj ) );
return RestrictedPermNC( g, info.news[ prj!.component ] )
^ ( info.perms[ prj!.component ] ^ -1 );
end );

#############################################################################
##
#M PreImagesRepresentativeNC( <prj>, <g> ) . . . . . . . . . . of projection
##
InstallMethod( PreImagesRepresentativeNC,"perm subdirect product projection",
FamRangeEqFamElm,
[ IsProjectionSubdirectProductWithEmbeddingsPermGroup,
IsMultiplicativeElementWithInverse ], 0,
function( prj, img )
local S,
elm, # preimage of <img> under <prj>, result
info, # info record
phi1, phi2; # homomorphisms of components

S := Source( prj );
info := SubdirectProductWithEmbeddingsInfo( S );

# get the homomorphism
phi1 := info.homomorphisms[1];
phi2 := info.homomorphisms[2];

# compute the preimage
if 1 = prj!.component then
elm := img ^ info.perms[1]
* PreImagesRepresentativeNC(phi2,img^phi1) ^ info.perms[2];
else
elm := img ^ info.perms[2]
* PreImagesRepresentativeNC(phi1,img^phi2) ^ info.perms[1];
fi;

# return the preimage
return elm;
end );

#############################################################################
##
#M KernelOfMultiplicativeGeneralMapping( <prj> ) . . . . . . . of projection
##
InstallMethod( KernelOfMultiplicativeGeneralMapping,
"perm subdirect product projection",true,
[ IsProjectionSubdirectProductWithEmbeddingsPermGroup ], 0,
function( prj )
local D, i, info;

D := Source( prj );
info := SubdirectProductWithEmbeddingsInfo( D );
i := 3 - prj!.component;
return SubgroupNC( D, OnTuples
( GeneratorsOfGroup( KernelOfMultiplicativeGeneralMapping(
info.homomorphisms[ i ] ) ),
info.perms[ i ] ) );
end );


#############################################################################
##
#M ViewObj( <prj> ) . . . . . . . . . . . . . . . . . . . . view projection
##
InstallMethod( ViewObj,
"for projection from subdirect product",
true,
[ IsProjectionSubdirectProductWithEmbeddingsPermGroup ], 0,
function( prj )
Print( Ordinal( prj!.component ), " projection of " );
View( Source( prj ) );
end );


#############################################################################
##
#M PrintObj( <prj> ) . . . . . . . . . . . . . . . . . . . print projection
##
InstallMethod( PrintObj,
"for projection from subdirect product",
true,
[ IsProjectionSubdirectProductWithEmbeddingsPermGroup ], 0,
function( prj )
Print( "Projection( ", Source( prj ), ", ", prj!.component, " )" );
end );

#############################################################################
## method copied from grpdpc.gi
##
#############################################################################
##
#M SubdirectProductWithEmbeddingsOp( <G1>, <G2>, <phi1>, <phi2> )
##
InstallMethod( SubdirectProductWithEmbeddingsOp,"pcgroup", true,
[ IsPcGroup, IsPcGroup, IsGroupHomomorphism, IsGroupHomomorphism ], 0,
function( G, H, gh, hh )
local pg,ph,kg,kh,ig,ih,mg,mh,S,info;
pg:=Pcgs(G);
ph:=Pcgs(H);
kg:=KernelOfMultiplicativeGeneralMapping(gh);
kh:=KernelOfMultiplicativeGeneralMapping(hh);
ig:=InducedPcgs(pg,kg);
ih:=InducedPcgs(ph,kh);
mg:=pg mod ig;
mh:=List(mg,i->PreImagesRepresentativeNC(hh,Image(gh,i)));
pg:=Concatenation(mg,ig,List(ih,i->One(G)));
ph:=Concatenation(mh,List(ig,i->One(H)),ih);
S:=SubdirProdPcGroups(G,pg,H,ph);
pg:=GroupHomomorphismByImagesNC(S[1],G,S[2],pg);
ph:=GroupHomomorphismByImagesNC(S[1],H,S[2],ph);
S:=S[1];
info:=rec(groups:=[G,H],
homomorphisms:=[gh,hh],
projections:=[pg,ph]);
SetSubdirectProductWithEmbeddingsInfo(S,info);
return S;
end);


#############################################################################
##
#E groups.gi . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here