# [GAP Forum] parabolic and Borel subgroups

David Joyner wdj at usna.edu
Wed Nov 24 11:28:03 GMT 2004

```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

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

>Dear forum,
>
>Is there any way to get the parabolic subgroups and the Borel subgroups of
>SL(2,7)? How?
>
>
>
>Thanks
>
>
>
>Univ. Of Science And Technology Of China,Dept Of Math.
>
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```