[GAP Forum] Question
Lisette Brillemans
lisette.brillemans at mensa.nl
Mon Jul 19 09:27:11 BST 2010
Dear Dan, dear Forum,
Thank you for your reply.
This does it indeed. But:
gap> G := Group(PermList(List([1..10], i->(i mod 10)+1));
is a very long and complicated line. Furthermore, what does NOT work (of
course...) is:
gap> G := SymmetricGroup(PermList(List([1..10], i->(i mod 10)+1));
So I would like to ask the forum again: Is it possible to do something
like (and how??):
gap> G:=Group([1..10]);
gap? G:=SymmetricGroup([1..10]);
etc.
(and especially with 100 instead of 10 and so.)
with regards,
Lisette
> Dear Lisette, Dear Forum,
>
> On Mon, Jul 19, 2010 at 8:57 AM, Alexander Hulpke <ahulpke at gmail.com>
> wrote:
> Dear GAP Forum,
>
> On Jul 18, 2010, at 3:15 PM, Lisette Brillemans wrote:
>
> > Is there a command to enter a group like
> >
> > S:=Group((1,2,3,4,5,6,7,8,9,10)); at once.
> >
> > For instance a command like:
> >
> > S:=Group([1..10]) or so?
>
> If you just want a cyclic group you can use
> CyclicGroup(IsPermGroup,10);
>
> Alternatively, you could use "List" to construct a list describing the
> permutation you are interested in:
> gap> x := List([1..10], i->(i mod 10)+1);
> [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 1 ]
> (this list means that 1 goes to x[1]=2, 2 goes to x[2] = 3, etc. Then
> use PermList to turn it into a permutation:
> gap> PermList(x);
> (1,2,3,4,5,6,7,8,9,10)
> see http://www.gap-system.org/Manuals/doc/htm/ref/CHAP040.htm#SECT004 for the documentation for PermList. We then use Group to construct the group generated by that permutation:
> gap> G := Group(PermList(x));
> Group([ (1,2,3,4,5,6,7,8,9,10) ])
> gap> Size(G);
> 10
>
>
> Hope this helps.
>
>
> Kind regards,
> Dan
>
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