[GAP Forum] listing simple groups

[Hulpke,Alexander]

Dear Keith,

> On Dec 6, 2019, at 6:54 AM, R. Keith Dennis <dennis at rkd.math.cornell.edu> wrote:
> 
> Dear Alexander,
> 
> thanks for the reply.  Yes, I know that, but that defeats one of my
> aims which is to determine the position number of a given simple
> group.
> 
> Of course there are other ways to do this (other programs), but since
> I know how to use GAP, this is the easiest way (for me).  I guess I
> can just automate doing this by intervals (rather than pasting
> together the data by hand as I had done earlier).
> 
> By your suggestion I could create the psl2 data separately and then
> "shuffle" the two pieces together (in the correct order) using a
> separate program.  I'll do this if I can't reach 10^18 otherwise.

If it is a single use, you could temporarily edit
grp/simple.gi

which creates the PSL2 specifically in line 681. Instead of creating the group, return the order. Then you do not need to bother with the finite fields.

All the best,

   Alexander

> 
> I had sort of hoped there was a cleaner way, which I was not aware of.
> 
> Thanks again!
> 
> Keith
> 
> 
> "Hulpke,Alexander" <Alexander.Hulpke at colostate.edu> wrote:
> 
>> Dear Keith, Dear Forum,
>> 
>>>   it:=SimpleGroupsIterator(1);;
>>> 
>>> runs out of memory at a little over 20,000 with using gap -o 200g.
>>> 
>>> So I presume it's keeping all the smaller groups, or at least some information 
>>> about them.  How do I remove all the older stuff from memory as I go along?
>> 
>> GAP is not keeping the groups, but it is keeping data about the finite fields created, and PSL2’s will create a lot of them. (There is no way to avoid this — finite field data is never cleaned out once the finite field was created.)
>> 
>> However in many cases one can deal with PSL2 in other ways, and thus there is an option to iterate through simple groups *excluding* psl2:
>> 
>> it:=SimpleGroupsIterator(1:nopsl2);;
>> 
>> which (I hope) will resolve the memory issue.
>> 
>> Best,
>> 
>> Alexander (Hulpke)
>> 
>> -- Colorado State University, Department of Mathematics,
>> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
>> email: hulpke at colostate.edu, Phone: ++1-970-4914288
>> http://www.math.colostate.edu/~hulpke
>> 
>>