Dear Alejandra, On Sun, Sep 04, 2016 at 08:16:31PM -0300, Alejandra Alderete wrote: > > I need to work with groups of hight order and my computer isn't potency o > capacity , I don't know. I am sending the algorithm. I need to find the > regular subgroups of the Symmetric Group S_24 isomorphic to S_4. > > gap> s4 := SymmetricGroup (4); > gap> s24 := SymmetricGroup (24); > gap> homo := AllHomomorphisms (s4, s24);; > gap> inj :=Filtered (homo, function (v) return IsInjective (v)= true ; end); > gap> img := List (inj, x-> Image (x, s4)); > gap> reg := Filtered (img, function (v) return IsRegular(v)= true ; end);
This would be a hopelessly long list. There are 24!/576 such subgroups in S_24. On the other hand constructing one copy is very easy, just let S_4 act on itself. gap> S4:=SymmetricGroup(4); Sym( [ 1 .. 4 ] ) gap> Action(S4,Elements(S4),OnRight); Group([ (1,10,17,19)(2,9,18,20)(3,12,14,21)(4,11,13,22)(5,7,16,23)(6,8,15,24), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,15)(14,16)(17,18) (19,21)(20,22)(23,24) ]) Hope this helps, Dmitrii. > > > > best regards > > Alejandra _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
