Dear GAP Forum, I would appreciate if any of you could provide me code (or suggest a package) that would help construct these groups for a positive integer n and a prime power q of prime p. If I have the code, I should be able to tweak it to construct the variants. I am not too concerned about computational efficiency:
(1) General semilinear group Gamma L(n,q), defined as semidirect product with base GL(n,q) and acting group the automorphism group of F_q (i.e., the Galois group of F_q over F_p). I'm also interested in constructing variants where the base group is taken as SL(n,q), PGL(n,q), or PSL(n,q), and also variants where we take a subgroup of the Galois group rather than the whole Galois group. (2) Outer linear group OL(n,q), defined as the semidirect product of GL(n,q) by a cyclic group of order two where the non-identity element acts by the transpose-inverse map. I also want to consider variants where the base group is taken as SL(n,q) instead of GL(n,q), as well as the variant where q = p^2 and we take the semidirect product by a cyclic group of order two acting by the conjugate-transpose-inverse. (3) General affine group denoted GA(n,q) or AGL(n,q) defined as the semidirect product of the n-dimensional vector space over F_q by GL(n,q) with its natural action. I also want to construct semidirect products for chosen subgroups of GL(n,q), and more generally, semidirect products associated with n-dimensional representations of groups over F_q. Thank you! Vipul _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
