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Not all finitely generated magmas are groups #2276

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Not all finitely generated magmas are groups #2276

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14 changes: 9 additions & 5 deletions lib/magma.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -652,13 +652,17 @@ InstallOtherMethod( MagmaWithOneByGenerators,
#M MagmaWithInversesByGenerators( <gens> ) . . . . . . . . for a collection
##
MakeMagmaWithInversesByFiniteGenerators:=function(family,gens)
local M;
local M, filter;
if not IsBound(family!.defaultMagmaWithInversesByGeneratorsType) then
filter := IsMagmaWithInverses and IsAttributeStoringRep
and HasGeneratorsOfMagmaWithInverses;
# check if the family implies associativity, and hence that the
# final magma is a group
if IS_SUBSET_FLAGS(family!.IMP_FLAGS, FLAGS_FILTER(IsAssociativeElementCollection)) then
filter := filter and IsFinitelyGeneratedGroup;
fi;
family!.defaultMagmaWithInversesByGeneratorsType :=
NewType( FamilyObj( gens ),
IsMagmaWithInverses and IsAttributeStoringRep
and HasGeneratorsOfMagmaWithInverses
and IsFinitelyGeneratedGroup);
NewType( FamilyObj( gens ), filter );
fi;

M:=rec();
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12 changes: 12 additions & 0 deletions tst/testbugfix/2018-03-21-MagmaWithInversesByGenerators.tst
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@@ -0,0 +1,12 @@
# GAP used to set the IsFinitelyGeneratedGroup property for every finitely
# generated magma-with-inverses, even those which are not groups.
gap> A:=[[1,2,3,4],[2,1,4,2],[3,4,1,3],[4,2,3,1]];
[ [ 1, 2, 3, 4 ], [ 2, 1, 4, 2 ], [ 3, 4, 1, 3 ], [ 4, 2, 3, 1 ] ]
gap> M:=MagmaWithInversesByMultiplicationTable(A);
<magma-with-inverses with 4 generators>
gap> IsFinitelyGeneratedGroup(M);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `IsFinitelyGeneratedGroup' on 1 argument\
s
gap> IsGroup(M);
false