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Not all finitely generated magmas are groups (alternative to PR #2276) #2311

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Mar 29, 2018
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Not all finitely generated magmas are groups (alternative to PR #2276) #2311

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6 changes: 4 additions & 2 deletions lib/magma.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -657,13 +657,15 @@ local M;
family!.defaultMagmaWithInversesByGeneratorsType :=
NewType( FamilyObj( gens ),
IsMagmaWithInverses and IsAttributeStoringRep
and HasGeneratorsOfMagmaWithInverses
and IsFinitelyGeneratedGroup);
and HasGeneratorsOfMagmaWithInverses);
fi;

M:=rec();
ObjectifyWithAttributes( M,family!.defaultMagmaWithInversesByGeneratorsType,
GeneratorsOfMagmaWithInverses, AsList( gens ) );
if HasIsAssociative( M ) and IsAssociative( M ) then
SetIsFinitelyGeneratedGroup( M, true );
fi;
return M;
end;

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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