[GAP Forum] Semi Direct Product

[Asst. Prof. Dmitrii (Dima) Pasechnik]

On 21 January 2012 22:34, Ashkan Ramiz <ashkanramiz at yahoo.com> wrote:
> Dear Gap Forum,
>
> How we can write the following groups in Gap?
>
> 1) Semi direct product G by H where G=DirectProduct(Z_2, Z_2) and H=PSL(2,7)
>
> 2) Semi direct product H by G where H=PSL(2,7) and G=DirectProduct(Z_2, Z_2)

When G is normal, such a semidirect product is direct, as H cannot act on G.

When H is normal, such a group is either the direct product, or G acts
on H, inducing an outer order 2 automorphism of H.
Thus you will get (H:Z_2)xZ_2, i.e. PGL(2,7)xZ_2.
>
> All the best,
> Ashkan

Best,
Dmitrii

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