[GAP Forum] needs help in programming for an integral power.

[Max Horn]

Dear Fawad Hayat,

from you description it is not really clear what you want to compute; nor does your pseudo code snippet make much sense to me. 

> On 27. Jul 2020, at 05:53, Fawad Hayat <fawadhayat05 at gmail.com> wrote:
> 
> Hello everbody,
> 
> I’m writing a program in GAP for group elements, that any two elements of a
> group G are an integral power of one another, i.e., for any x, y ∈ G, then x
> n=y or yn=x, where n is any positive integer.

If you really just want to check for a given group G whether

 \forall x,y\in G \exists n>0:  x^n=y  or y^n=x

Then you don't need to write length GAP programs for this: You can easily characterize these groups by hand: they certainly must be cyclic; now you just need to check which cyclic groups satisfy this property (I'll leave it to you to figure out which exactly, it's a fun exercise).

Or perhaps you really want to compute something else; then you should try to carefully write up what it is you really are asking, mathematically, so that we have a chance of understanding and helping.

Best regards
Max Horn


> But it has some problems. *I
> don’t know where to write the value “n.”*  I’ll be very grateful if it can
> be written more simply.
> 
> 
> 
> f := f unction(G)
> 
> local x; y; M; MM; i; j; s; d; n;
> 
> M:= []; MM:= []; s:= 0; d:= [];
> 
> *for n in Integers do*
> 
> for x in Elements(G) do
> 
> for y in Elements(G) do
> 
> if x^n = y  then
> 
> Add(M; 1);
> 
> else
> 
> Add(M; 0);
> 
> fi;
> 
> od;
> 
> od;
> 
> Add(MM;M); M := [];
> 
> od;
> 
> Print(MM);
> 
> for i in MM do
> 
> for j in i do
> 
> s:= s + j;
> 
> od;
> 
> Add(d; s); s := 0;
> 
> od;
> 
> Print(d);
> 
> return;
> 
> end;
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum