[GAP Forum] Question

[Dan Roozemond]

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