[GAP Forum] Certain Subgroups of SL(3, q) of Order q^3 for small q

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear Sandeep,

Suppose F_q is k-fold extension of F_p, for p prime. Then, if x1,..,xk
are generators of
F_q over F_p,
S is generated by matrices by 2k matrices, namely
[[1 xj 0],
[0 1 0],
[0 0 1]], with j=1,...k, and

[[1 0 0],
[0 1 xj],
[0 0 1]], with j=1,...k.


and similarly for T (take the transposes of generators above).

Hope this helps,
Dmitrii



On 29 January 2011 23:05, Sandeep Murthy <sandeepr.murthy at gmail.com> wrote:
> Hello,
>
> If G = SL(3,q), the special linear group over the finite field F_q, then
> I am interested in the following subgroups:
>
> S = { set of all upper triangular matrices in G with 1s on the diagonal, and elements x,y,z above the diagonal},
> T = { set of all lower triangular matrices in G with 1s on the diagonal, and elements x,y,z below the diagonal}.
>
> How can I define these subgroups in GAP for specific small values of q, like 2, 3, 4 etc.?
>
> Sincerely, Sandeep.
>
>

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