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Fix bug in IsFinitelyGeneratedGroup method #2275

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Merged
fingolfin merged 1 commit into from
Mar 21, 2018
Merged

Fix bug in IsFinitelyGeneratedGroup method #2275

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10 changes: 7 additions & 3 deletions lib/grp.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -18,9 +18,13 @@
#M IsFinitelyGeneratedGroup( <G> ) . . test if a group is finitely generated
##
InstallImmediateMethod( IsFinitelyGeneratedGroup,
IsGroup and HasGeneratorsOfGroup, 0,
G -> IsFinite( GeneratorsOfGroup( G ) ) );

IsGroup and HasGeneratorsOfGroup,
function( G )
if IsFinite( GeneratorsOfGroup( G ) ) then
return true;
fi;
TryNextMethod();
end );

#############################################################################
##
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17 changes: 17 additions & 0 deletions tst/testbugfix/2018-03-21-IsFinitelyGeneratedGroup.tst
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@@ -0,0 +1,17 @@
# There was an incorrect method for IsFinitelyGeneratedGroup which assumed
# that a group given by an infinite generating set is not finitely generated,
# which is of course false: any finitely generated infinite group is generated
# by its set of elements.
#
# Test that this is not the case anymore:
gap> F:=FreeGroup(1);;
gap> G:=SubgroupShell(F);
Group(<free, no generators known>)
gap> SetGeneratorsOfGroup(G, Enumerator(F));

# We are defensive: GAP should either not know that G is finitely generated
# (that's the situation right now), or, if it ever is improved to handle this
# case, it should correctly determine that G = F is finitely generated (even
# cyclic)
gap> not HasIsFinitelyGeneratedGroup(G) or IsFinitelyGeneratedGroup(G);
true