[GAP Forum] applying permutation to subset: strange problem?

[Frederic Vanhove]

Dear members of the Forum,


I was experimenting with some permutation groups, and noticed that I had 
some difficulties to have GAP compute the image of a subset under a 
certain permutation.

In particular: the following works just fine:

g:=AllPrimitiveGroups(DegreeOperation,12)[2];
h:=Stabilizer(g,[1,2],OnSets);
w:=Random(h);
orbits:=Orbits(h,[1..12]);
OnSets(orbits[1],w);

while this produces an error:


g:=AllPrimitiveGroups(DegreeOperation,12)[2];
h:=Stabilizer(g,[1,2],OnSets);
w:=Random(h);
orbits:=Orbits(h,[1..12]);
OnSets(orbits[2],w);



The respective outputs are:

gap> g:=AllPrimitiveGroups(DegreeOperation,12)[2];
M(12)
gap> h:=Stabilizer(g,[1,2],OnSets);
Group([ (5,9,6,11)(7,12,10,8), (5,10,6,7)(8,9,12,11), 
(4,7)(5,8)(6,9)(11,12),
   (4,8)(5,9)(6,7)(10,11), (3,4,10,5)(6,7,9,8), (1,2)(4,12)(5,11)(6,10) ])
gap> w:=Random(h);
(3,12)(4,7,10,5,8,6,11,9)
gap> orbits:=Orbits(h,[1..12]);
[ [ 1, 2 ], [ 3, 4, 7, 8, 10, 12, 5, 6, 9, 11 ] ]
gap> OnSets(orbits[1],w);
[ 1, 2 ]

and:

gap> g:=AllPrimitiveGroups(DegreeOperation,12)[2];
M(12)
gap> h:=Stabilizer(g,[1,2],OnSets);
Group([ (5,9,6,11)(7,12,10,8), (5,10,6,7)(8,9,12,11), 
(4,7)(5,8)(6,9)(11,12),
   (4,8)(5,9)(6,7)(10,11), (3,4,10,5)(6,7,9,8), (1,2)(4,12)(5,11)(6,10) ])
gap> w:=Random(h);
(3,7,6,10,4,11,5,9)(8,12)
gap> orbits:=Orbits(h,[1..12]);
[ [ 1, 2 ], [ 3, 4, 7, 8, 10, 12, 5, 6, 9, 11 ] ]
gap> OnSets(orbits[2],w);
OnSets: <set> must be a set (not a list (plain,cyc,nsort,imm))
not in any function
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can replace <set> via 'return <set>;' to continue

This is rather strange, as there seems to be no real difference between 
orbits[1] and orbits[2] (I mean: in the way they have been stored?)

Kind regards,
Frédéric