On 21 January 2012 22:34, Ashkan Ramiz <ashkanra...@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 CONFIDENTIALITY: This email is intended solely for the person(s) named and may be confidential and/or privileged. If you are not the intended recipient, please delete it, notify us and do not copy, use, or disclose its content. Towards A Sustainable Earth: Print Only When Necessary. Thank you. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
