[GAP Forum] size of permutation groups

[Allan Adler]

Jack Schmidt wrote:
>You should have no trouble with n=5,6,7,8,9.  Here is some code which 
>constructs the permutations K and * on n! and checks if they generate 
>the symmetric group of size (n!)!.  The code below runs in about one minute.
[snip]
>Outputs:
>3: false
>4: true
>5: true
>6: false
>7: false
>8: false
>9: false
>n=10 is also false, but took more in the 5 minute range. 3-8 is a few 
>seconds, and 3-9 is about a minute.  These are on an 1.5ghz pc.

Thanks for computing this. The most powerful machine I have is an old
HP Pavilion with 192MB ram (+400 MB swap space) and running at about
530 MHz. I ran your code and, for n=3,4,5, it ran in about the same time
that my code had run. For n=6, I let it run for about 8 hours and, when
I checked on it, the program had crashed for lack of system resources.

I did, however, run Dima Pasechnik's code and it quickly indicated that
for n=6 one probably doesn't get the full symmetric group.

At any rate, now I'd like to know what groups one does get, but it is
pretty clear that I'm not equipped to work on it, for lack of suitable
computer facilities, and I can't afford to buy better ones. So, if someone
does figure out more about these groups, I hope they will let me know
about them.
-- 
Allan Adler <ara at zurich.csail.mit.edu>
* Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and
* comments do not reflect in any way on MIT. Also, I am nowhere near Boston.