On Tue, Jun 12, 2018 at 5:48 AM riccardoventrella < [email protected]> wrote:
> Hello, > I'm having fun with Prof. Joyner Adventures in Group Theory, and I was > experimenting with the smallest > non-abelian simple group, i.e. PSL(2,5). Actually, it can be applied to > the projective line P1 over the finite field F5. > > The amazing thing to me is this map actually permutes the projective line > elements, acting as a automorphism group. > > I know how to realise PSL(2,5) in SAGE but I was wondering if there's a > way to define a projective line over F5 and see > its elements permuted by PSL(2,5) action in some way. > > Here's an example with GF(8) instead of GF(5): sage: F = GF(*8*) sage: P1F = ProjectiveSpace(*1*,F) sage: P1Flist = P1F.rational_points() sage: G = PSL(*2*,F) sage: Gaction = *lambda* x: P1Flist[g(P1Flist.index(x)+*1*)+*1*] sage: a = P1F.rational_points()[*2*] sage: Gaction(a) (1 : 0) sage: a = P1F.rational_points()[*3*] sage: Gaction(a) (z3 + 1 : 1) This works because G is a subgroup of a symmetric group. > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
