[GAP Forum] IsSubgroup(FactorGroup(G/N),FactorGroup(H/N));

[Stephen Linton]

Dear Iopo Apelo Kosho,

Your analysis of the problem in the first paragraph below is correct. FactorGroup in GAP returns a group isomorphic to the relevant factor 
but, in general, multiple calls to FactorGroup produce independent groups. 

The solution is to instead use the factor homomorphism, which allows you to connect everything together.

So,  you might replace your line

> if notIsNearlySPermutable(FactorGroup(g,pn[i]),FactorGroup(m[j],pn[i]))

by something like

phi := NaturalHomomorphismByNormalSubgroup(g, pn[i]);
f1 := ImagesSource(phi);
f2 := Image(phi, m[j]);
if not IsNearlySPermutable(f1, f2) then

The first two lines can actually be moved outside the j loop, saving some work.

	Steve


> On 22 Aug 2018, at 21:25, lopo apelo kosho <helo_07 at yahoo.com> wrote:
> 
> Dear friends;I would be very grateful if you advice/help m to handle a situation related to GAP: 
> If N is a subgroup of H, H is subgroup of G, and N is normal in G; then H/N is subgroup of G/N. The problem is that GAP does not recognize it so. 
> I have constructed the following code to check quotient closeness for some property, The code is: 
> IsQClosedNSPSubgroups:=function(g) local pn,nsp,i,j,m;
> 
> if IsAbelian(g) then return true;
> 
> fi;
> 
> pn:=ProperNormalSubgroups(g);
> 
> if Size(NormalSubgroups(g))=Size(Subgroups(g)) thenreturn true;
> 
> fi;
> 
> nsp:=NSPSubgroups(g);
> 
> for i in [1..Size(pn)] do
> 
> m:=Filtered(nsp,x->IsSubgroup(x,pn[i]));
> 
> for j in [1..Size(m)] do 
> 
> if notIsNearlySPermutable(FactorGroup(g,pn[i]),FactorGroup(m[j],pn[i]))
> 
> then return false; 
> 
> fi;                                                                  
> 
> od;
> 
> od;
> 
> return true;
> 
> end;
> 
> 
> THE ERROR MESSAGE IS:
> Error, no method found! For debugging hints type ?Recovery from NoMethodFoundError, no 1st choice method found for `IsNormalOp' on 2 arguments called fromoper( super, sub ) at /proc/cygdrive/C/gap4r7/lib/domain.gd:439 called fromIsNormal( g, h ) at *stdin*:427 called fromIsNearlySPermutable( FactorGroup( g, pn[i] ), FactorGroup( m[j], pn[i] ) ) at *stdin*:685 called from<function "IsQClosedNSPSubgroups">( <arguments> ) called from read-eval loop at line 691 of *stdin*you can 'quit;' to quit to outer loop, oryou can 'return;' to continue
> 
> Thank you for your advice.
>    
>   
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum