[GAP Forum] Low index normal subgroups

[Marco Costantini]

Dear Primoz and dear gap forum, 
 
Scrive Primoz Moravec <primoz.moravec at fmf.uni-lj.si>: 
> what is the best way to compute normal subgroups of low index in a given 
> finitely presented group? 
 
(I don't know the best way but I can suggest a way to try.) 
 
Look at the functions in the manual in the paragraph Groups - Sets of 
Subgroups: maybe the functions MaximalNormalSubgroups or NormalSubgroups are 
what you need. 
 
Such functions may not terminate in the case that your group is not finite... 
in this case, and if it make sense for your problem, you can consider some 
finite quotient of your group, and calculate MaximalNormalSubgroups or 
NormalSubgroups in it.  
 
There are package to calculare the p-/nilpotent/polyciclic/solvable quotients 
of finitely presented groups (see the packages anupq, nq, etc.). the kind of 
quotient to calculate depends on your problem. 
 
If otherwise your finitely presented group G is finite, it could be better to 
convert it into a polycyclic or permutation group, for efficiency, before 
doing any other computation. 
 
Image(IsomorphismSpecialPcGroup(G));  (if G is solvable) 
Image(IsomorphismPermGroup(G));       (otherwise) 
 
Best Regards, 
Marco