Dear Benjamin,
On 29.01.2014, at 16:27, Benjamin Sambale <benjamin.samb...@gmail.com> wrote:
> Dear GAP users,
>
> I'm using GAP 4.7.2 and just ran into the following strange behavior:
>
> G:=AbelianGroup([4,4,4]);;
> A:=AutomorphismGroup(G);;
> x:=First(A,a->Order(a)<>Size(Group(a)));
> [ f1*f2*f3, f5, f1*f2*f6 ] -> [ f1, f1*f2*f4*f5*f6, f2*f3*f6 ]
>
> I thought that the order of an element is the same as the size of the
> generated group?? Indeed:
>
> x^Order(x);
> Pcgs([ f1, f2, f3, f4, f5, f6 ]) -> [ f1, f2, f3, f4, f4*f5*f6, f6 ]
>
> Any ideas?
This is a bug in GAP :-(. It will be fixed in the next GAP release. In the
meantime, you can paste this code into your GAP session to fix the issue:
InstallMethod(Order,"for automorphisms",true,[IsGroupHomomorphism],0,
function(hom)
local map,phi,o,lo,i,start,img;
o:=1;
phi:=hom;
map:=MappingGeneratorsImages(phi);
i:=1;
while i <= Length(map[1]) do
lo:=1;
start:=map[1][i];
img:=map[2][i];
while img<>start do
img:=ImagesRepresentative(phi,img);
lo:=lo+1;
# do the bijectivity test only if high local order, then it does not
# matter
if lo=1000 and not IsBijective(hom) then
Error("<hom> must be bijective");
fi;
od;
if lo>1 then
o:=o*lo;
if i<Length(map[1]) then
phi:=phi^lo;
map:=MappingGeneratorsImages(phi);
i:=0;
fi;
fi;
i:=i+1;
od;
return o;
end);
Thanks for the report,
Max
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