[GAP Forum] Intersections

[Motalane, John]

Dear All

Hoping that you are well.

I am working with the alternating group A_11. I am looking at the
intersection of five groups as done in CAP below. I see that the
intersection lies in these three orbits (120, 360 and 720). I can easily
calculate (see programme below) that the intersection of  conjugacy classes
for these five maximal subgroups has candidates of orders 72 and 120. My
question is that are these the only candidates, if not how do we find other
candidates? One can show the best method for finding the intersection of
conjugacy classes for maximal subgroups.

Thanks in advance

Regards John

gap> a:= (1,2,3);;
gap> b:= (3,4,5,6,7,8,9,10,11);;
gap> g:=Group(a,b);;
gap> mx:= MaximalSubgroupClassReps( g );;
gap> m11:= Filtered( mx, x -> Size(x) = 2^7*3^4 * 175);;
gap> m22:= Filtered( mx, x -> Size(x) = 2^7*3^4 * 35);;
gap> m33:= Filtered( mx, x -> Size(x) = 2^7*3^3 * 35);;
gap> m44:= Filtered( mx, x -> Size(x) = 2^6*3^3 * 35);;
gap> m55:= Filtered( mx, x -> Size(x) = 2^6*3^3 * 25);;
gap> m66:= Filtered( mx, x -> Size(x) = 2^4*3^2 * 55);;
gap> m77:= Filtered( mx, x -> Size(x) = 2^3*3^2 * 110);;
gap> o:=Orbit(g,m11[1]);;
gap>
i12345:=List(o,x->Intersection(x,(Intersection(m22[1],m33[1],m44[1],m55[1]))));;
gap> List(i12345,Size);
[ 360, 120, 120, 120, 120, 120, 120, 720, 720, 720, 360 ]

gap> repeat x:= Intersection( m11[1], m22[1],m33[1],m44[1],m55[1]^Random(g)
);
> until Size( x ) <> 1;
gap> Size(x);
72
gap> repeat x:= Intersection( m11[1], m22[1],m33[1],m44[1],m55[1]^Random(g)
);
> until Size( x ) <> 72;
gap> Size(x);
120
gap> repeat x:= Intersection( m11[1], m22[1],m33[1],m44[1],m55[1]^Random(g)
);
> until Size( x ) <> 120;
gap> Size(x);
72

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