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Fix implication for IsSubsetLocallyFiniteGroup; and teach Units(GF(q)) its size #2220

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Mar 2, 2018
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Fix implication for IsSubsetLocallyFiniteGroup; and teach Units(GF(q)) its size #2220

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ffb9e3b
Fix implication for IsSubsetLocallyFiniteGroup
fingolfin Feb 28, 2018
40fa874
Teach Units(GF(q)) its size
fingolfin Mar 1, 2018
355cfe7
IsFFEMatrixGroup implies IsSubsetLocallyFiniteGroup
fingolfin Mar 1, 2018
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9 changes: 8 additions & 1 deletion lib/fieldfin.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -79,7 +79,14 @@ InstallMethodWithRandomSource( Random,
InstallMethod( Units,
"for a finite field",
[ IsField and IsFinite ],
F -> GroupByGenerators( [ PrimitiveRoot( F ) ] ) );
function ( F )
local G;
G := GroupByGenerators( [ PrimitiveRoot( F ) ] );
if HasSize( F ) then
SetSize( G, Size( F )-1 );
fi;
return G;
end );


#############################################################################
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5 changes: 3 additions & 2 deletions lib/grp.gd
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Expand Up @@ -253,9 +253,10 @@ InstallSubsetMaintenance( IsSubsetLocallyFiniteGroup,

#############################################################################
##
#M IsSubsetLocallyFiniteGroup( <G> ) . . . . . . . . . . for magmas of FFEs
#M IsSubsetLocallyFiniteGroup( <G> ) . . . for magmas with inverses of FFEs
##
InstallTrueMethod( IsSubsetLocallyFiniteGroup, IsFFECollection and IsMagma );
InstallTrueMethod( IsSubsetLocallyFiniteGroup,
IsFFECollection and IsMagmaWithInverses );


#############################################################################
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8 changes: 5 additions & 3 deletions lib/grpffmat.gd
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Expand Up @@ -30,13 +30,15 @@ DeclareSynonym( "IsFFEMatrixGroup", IsFFECollCollColl and IsMatrixGroup );

#############################################################################
##
#M IsFinite( <ffe-mat-grp> )
#M IsSubsetLocallyFiniteGroup( <ffe-mat-grp> )
##
## As a consequence, any IsFFEMatrixGroup in IsFinitelyGeneratedGroup
## automatically is also in IsFinite.
##
## *Note:* The following implication only holds if there are no infinite
## dimensional matrices.
##
InstallTrueMethod( IsFinite,
IsFFEMatrixGroup and IsFinitelyGeneratedGroup );
InstallTrueMethod( IsSubsetLocallyFiniteGroup, IsFFEMatrixGroup );


#############################################################################
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2 changes: 1 addition & 1 deletion lib/ring.gd
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Expand Up @@ -748,7 +748,7 @@ InstallFactorMaintenance( IsZeroMultiplicationRing,
## gap> Units( GaussianIntegers );
## [ -1, 1, -E(4), E(4) ]
## gap> Units( GF( 16 ) );
## <group with 1 generators>
## <group of size 15 with 1 generators>
## ]]></Example>
## </Description>
## </ManSection>
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29 changes: 29 additions & 0 deletions tst/testbugfix/2018-02-28-IsSubsetLocallyFiniteGroup.tst
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@@ -0,0 +1,29 @@
# there used to be a bad implication from IsFFECollection and IsMagma to
# IsSubsetLocallyFiniteGroup, which caused all finite fields to be in filter
# IsSubsetLocallyFiniteGroup -- verify this is not the case anymore.
gap> HasIsSubsetLocallyFiniteGroup(GF(2));
false
gap> HasIsSubsetLocallyFiniteGroup(GF(2^20));
false

# that implication was replaced by one from IsFFECollection and IsMagmaWithInverses
# to IsSubsetLocallyFiniteGroup -- verify that it works
gap> G:=Units(GF(2));;
gap> HasIsSubsetLocallyFiniteGroup(G);
true
gap> HasIsFinite(G);
true

#
gap> G:=Group(Z(2));;
gap> HasIsSubsetLocallyFiniteGroup(G);
true
gap> HasIsFinite(G);
true

#
gap> G:=Group(Z(2^20));;
gap> HasIsSubsetLocallyFiniteGroup(G);
true
gap> HasIsFinite(G);
true