[GAP Forum] Question

[Lisette Brillemans]

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 
>