[GAP Forum] parabolic and Borel subgroups

[David Joyner]

Hi Saad Bedaiwi:

p:=7;
G:=SL(2,p);
a0:=[ [ Z(p), Z(p) ], [ Z(p)*0, Z(p)^(-1) ] ];
n0:=[ [ Z(p)0, Z(p) ], [ Z(p)*0, Z(p)0 ] ];
B:=Group([a0,n0]);
IsSubgroup(G,B);


On the other hand, it is convenient often to first convert the group
SL(2,7) into a permutation group. For this use,

G:=SL(2,p);
iso:=IsomorphismPermGroup(G);
G0:=Image(iso);
a0:=Image(iso,[ [ Z(p), Z(p) ], [ Z(p)*0, Z(p)^(-1) ] ]);
n0:=Image(iso,[ [ Z(p)0, Z(p) ], [ Z(p)*0, Z(p)0 ] ]);
B:=Group([a0,n0]);; # the Borel as a permutation group

Hope this helps. - David Joyner

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

saad bedaiwi wrote:

>Dear forum,
>
>Is there any way to get the parabolic subgroups and the Borel subgroups of
>SL(2,7)? How? 
>
>
>
>Thanks
>
>
>-----------------                Saad.A.Bedaiwi    
>
>Univ. Of Science And Technology Of China,Dept Of Math.
>
>Tel No : +86  551_3650275 -------------------
>
>
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