[GAP Forum] Forum Digest, Vol 199, Issue 10

[Fawad Hayat]

Thank you Sir, for your kind response. Actually, we have a definition of
the power graph of a group G,   “Two elements x, y of G being adjacent iff
one element is a power of the other, i.e., x^n=y or y^n=x.” So I would like
to find all those elements which satisfy this condition. In The following
program I need the set M and MM which I defined. If the following program
have some problems please correct that for me, I’ll be very grateful to
you.

Best regards,
Fawad.

On Tue, Jul 28, 2020 at 4:00 PM <forum-request at gap-system.org> wrote:

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> Today's Topics:
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>    1. Re: needs help in programming for an integral power. (Max Horn)
>    2. Re: needs help in programming for an integral power.
>       (Bill Allombert)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 27 Jul 2020 13:39:07 +0200
> From: Max Horn <horn at mathematik.uni-kl.de>
> To: Fawad Hayat <fawadhayat05 at gmail.com>
> Cc: GAP Forum <forum at gap-system.org>
> Subject: Re: [GAP Forum] needs help in programming for an integral
>         power.
> Message-ID:
>         <6C62711E-C134-4138-BF5F-E26BEE3C414E at mathematik.uni-kl.de>
> Content-Type: text/plain;       charset=utf-8
>
> 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
>
>
>
>
> ------------------------------
>
> Message: 2
> Date: Mon, 27 Jul 2020 17:32:10 +0200
> From: Bill Allombert <Bill.Allombert at math.u-bordeaux.fr>
> To: forum at gap-system.org
> Subject: Re: [GAP Forum] needs help in programming for an integral
>         power.
> Message-ID: <20200727153210.GE25720 at yellowpig>
> Content-Type: text/plain; charset=utf-8
>
> On Mon, Jul 27, 2020 at 11:53:11AM +0800, Fawad Hayat 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. 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.
>
> It seems your question is how to loop over the integers.
>
> You can do something like
>
> gap> for n in [1..10] do Print(n); od;
> 12345678910
>
> Cheers,
> Bill.
>
>
>
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> End of Forum Digest, Vol 199, Issue 10
> **************************************
>