[GAP Forum] Fwd: The other intersection

[Hulpke,Alexander]

Dear GAP Forum,

John Motalane wrote:

> On the group Sp(6,2), in order to get intersections. I used the below
> programme you provided which is working fine. To my suprise for the
> intersection of the maximal subgroup m2 and m8 of Sp(6,2), I could get only
> one candidate whose order is 42. If I try to get the other candidate if
> any, the computer couldn't end the calculations for hours. Should I
> conclude that this is the only candidate or I should exercise my patient.

Time alone does not prove it, but you can take intersections of m8[1] with all elememnts of the orbit of m2:


gap> o:=Orbit(g,m2[1]);;
gap> Length(o);
36

gap> ise:=List(o,x->Intersection(x,m8[1]));;
gap> List(ise,Size);
[ 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42,
  42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42 ]

In fact these intersections all lie in one G-Orbit:

gap> ForAll(ise,x->RepresentativeAction(g,ise[1],x)<>fail);
true

Best,

  Alexander Hulpke