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Transfer more properties (such as IsNaturalSL, InvariantQuadraticForm etc.) when conjugating matrix groups #6183

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Merged
fingolfin merged 6 commits into from
Jan 16, 2026
+90 −3
Merged

Transfer more properties (such as IsNaturalSL, InvariantQuadraticForm etc.) when conjugating matrix groups #6183

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d0fe30f
Make `IsFullSubgroupGLorSLRespectingBilinearForm` docs more specific
lgoettgens Dec 22, 2025
876fd71
Transfer more properties when conjugating matrix groups
lgoettgens Dec 19, 2025
6bf6e9f
Add test
lgoettgens Dec 22, 2025
1f3457e
Fix GroupMethodByNiceMonomorphismCollElm test
fingolfin Jan 13, 2026
1d343e7
Transfer nice mono
lgoettgens Jan 14, 2026
d16d1bd
Merge branch 'lg/matgrp-conjugate' of github.com:lgoettgens/gap into …
lgoettgens Jan 14, 2026
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7 changes: 5 additions & 2 deletions lib/grpmat.gd
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Expand Up @@ -345,7 +345,8 @@ DeclareAttribute( "InvariantBilinearForm", IsMatrixGroup );
## <Description>
## This property tests, whether a matrix group <A>matgrp</A> is the full
## subgroup of GL or SL (the property <Ref Prop="IsSubgroupSL"/> determines
## which it is) respecting the form stored as the value of
## which it is) in the right dimension over the (smallest) ring which
## contains all entries of its elements, respecting the form stored as the value of
## <Ref Attr="InvariantBilinearForm"/> for <A>matgrp</A>.
## </Description>
## </ManSection>
Expand Down Expand Up @@ -462,7 +463,9 @@ DeclareAttribute( "InvariantQuadraticForm", IsMatrixGroup );
## <Description>
## This property tests, whether the matrix group <A>matgrp</A> is the full
## subgroup of GL or SL (the property <Ref Prop="IsSubgroupSL"/> determines
## which it is) respecting the <Ref Attr="InvariantQuadraticForm"/> value
## which it is) in the right dimension over the (smallest) ring which
## contains all entries of its elements,
## respecting the <Ref Attr="InvariantQuadraticForm"/> value
## of <A>matgrp</A>.
## <Example><![CDATA[
## gap> g:= Sp( 2, 3 );;
Expand Down
64 changes: 64 additions & 0 deletions lib/grpmat.gi
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Expand Up @@ -1266,3 +1266,67 @@ InstallMethod( InvariantBilinearForm,
Q:= InvariantQuadraticForm( matgrp ).matrix;
return rec( matrix:= ( Q + TransposedMat( Q ) ) );
end );

#############################################################################
##
#M ConjugateGroup( <G>, <g> ) of a matrix group
##
InstallMethod( ConjugateGroup, "<G>, <g>", IsCollsElms,
[ IsMatrixGroup, IsMultiplicativeElementWithInverse ],
function( G, g )
local H, m, ginv, nice, conj;

H := GroupByGenerators( OnTuples( GeneratorsOfGroup( G ), g ), One( G ) );
UseIsomorphismRelation( G, H );
if HasIsGeneralLinearGroup( G ) then
SetIsGeneralLinearGroup( H, IsGeneralLinearGroup( G ) );
fi;
if HasIsSpecialLinearGroup( G ) then
SetIsSpecialLinearGroup( H, IsSpecialLinearGroup( G ) );
fi;
if HasIsSubgroupSL( G ) then
SetIsSubgroupSL( H, IsSubgroupSL( G ) );
fi;
if HasInvariantBilinearForm( G ) then
if not IsBound( ginv ) then
ginv := g^-1;
fi;
m := ginv * InvariantBilinearForm( G ).matrix * TransposedMat( ginv );
SetInvariantBilinearForm( H, rec( matrix := m ) );
fi;
if HasInvariantQuadraticForm( G ) then
if not IsBound( ginv ) then
ginv := g^-1;
fi;
m := ginv * InvariantQuadraticForm( G ).matrix * TransposedMat( ginv );
SetInvariantQuadraticForm( H, rec( matrix := m ) );
fi;
if IsSubset( FieldOfMatrixGroup( G ), FieldOfMatrixList( [ g ] ) ) then
if HasIsNaturalGL( G ) then
SetIsNaturalGL( H, IsNaturalGL( G ) );
fi;
if HasIsNaturalSL( G ) then
SetIsNaturalSL( H, IsNaturalSL( G ) );
fi;
if HasIsFullSubgroupGLorSLRespectingBilinearForm( G )
and IsFullSubgroupGLorSLRespectingBilinearForm( G ) then
SetIsFullSubgroupGLorSLRespectingBilinearForm( H, true );
fi;
if HasIsFullSubgroupGLorSLRespectingQuadraticForm( G )
and IsFullSubgroupGLorSLRespectingQuadraticForm( G ) then
SetIsFullSubgroupGLorSLRespectingQuadraticForm( H, true );
fi;
fi;
if HasNiceMonomorphism( G ) then
nice := NiceMonomorphism( G );
if not IsBound( ginv ) then
ginv := g^-1;
fi;
conj := GroupHomomorphismByFunction( H, G, y -> g*y*ginv, x -> ginv*x*g );
SetNiceMonomorphism( H, conj * nice );
if HasNiceObject( G ) then
SetNiceObject( H, NiceObject( G ) );
fi;
fi;
return H;
end );
20 changes: 20 additions & 0 deletions tst/testinstall/grp/classic-forms.tst
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Expand Up @@ -54,6 +54,8 @@ gap> grps:=[];;
gap> for d in [3,5,7] do
> for q in [2,3,4,5,7,8,9,16,17,25,27] do
> Add(grps, GO(d,q));
> Add(grps, GO(d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, GO(d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> od;
> od;
gap> ForAll(grps, CheckGeneratorsInvertible);
Expand All @@ -71,6 +73,10 @@ gap> for d in [2,4,6,8] do
> for q in [2,3,4,5,7,8,9,16,17,25,27] do
> Add(grps, GO(+1,d,q));
> Add(grps, GO(-1,d,q));
> Add(grps, GO(+1,d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, GO(-1,d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, GO(+1,d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> Add(grps, GO(-1,d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> od;
> od;
gap> ForAll(grps, CheckGeneratorsInvertible);
Expand All @@ -87,6 +93,8 @@ gap> grps:=[];;
gap> for d in [3,5,7] do
> for q in [2,3,4,5,7,8,9,16,17,25,27] do
> Add(grps, SO(d,q));
> Add(grps, SO(d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, SO(d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> od;
> od;
gap> ForAll(grps, CheckGeneratorsSpecial);
Expand All @@ -104,6 +112,10 @@ gap> for d in [2,4,6,8] do
> for q in [2,3,4,5,7,8,9,16,17,25,27] do
> Add(grps, SO(+1,d,q));
> Add(grps, SO(-1,d,q));
> Add(grps, SO(+1,d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, SO(-1,d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, SO(+1,d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> Add(grps, SO(-1,d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> od;
> od;
gap> ForAll(grps, CheckGeneratorsSpecial);
Expand All @@ -124,6 +136,8 @@ gap> grps:=[];;
gap> for d in [3,5,7] do
> for q in [2,3,4,5,7,8,9,16,17,25,27] do
> Add(grps, Omega(d,q));
> Add(grps, Omega(d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, Omega(d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> od;
> od;
gap> ForAll(grps, CheckGeneratorsSpecial);
Expand All @@ -141,6 +155,10 @@ gap> for d in [2,4,6,8] do
> for q in [2,3,4,5,7,8,9,16,17,25,27] do
> Add(grps, Omega(+1,d,q));
> Add(grps, Omega(-1,d,q));
> Add(grps, Omega(+1,d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, Omega(-1,d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, Omega(+1,d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> Add(grps, Omega(-1,d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> od;
> od;
gap> ForAll(grps, CheckGeneratorsSpecial);
Expand Down Expand Up @@ -191,6 +209,8 @@ gap> grps:=[];;
gap> for d in [2,4,6,8] do
> for q in [2,3,4,5,7,8,9,16,17,25,27] do
> Add(grps, Sp(d,q));
> Add(grps, Sp(d,q) ^ RandomInvertibleMat(d,GF(q)));
> Add(grps, Sp(d,q) ^ RandomInvertibleMat(d,GF(q^2)));
> od;
> od;
gap> ForAll(grps, CheckGeneratorsSpecial);
Expand Down
2 changes: 1 addition & 1 deletion tst/testinstall/mapping.tst
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Expand Up @@ -496,7 +496,7 @@ gap> g2:= SubgroupNC( g, [ A, B ] );; # need a parent
gap> HasIsHandledByNiceMonomorphism( g2 ); MayBeHandledByNiceMonomorphism( g2 );
false
true
gap> g2:= ConjugateGroup( g2, C );;
gap> g2:= ClosureGroup( g2, B );;
gap> HasIsHandledByNiceMonomorphism( g2 ); IsHandledByNiceMonomorphism( g2 );
true
true
Expand Down
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