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 -- --------------------------------------------------------------------------------------------------------------------------------------------------------------------- DISCLAIMER *** This message and any attachments are confidential and intended solely for the addressee. The following link will display the full disclaimer: http://www.ul.ac.za/disclaimer.jpg <http://www.ul.ac.za/disclaimer.jpg> *** -- ** ** **60 Years Anniversary Celebrations ** **For more information: **https://www.ul.ac.za/60 <https://www.ul.ac.za/60> _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
