[GAP Forum] Order of a group presentation

[Dima Pasechnik]

Dear Nick,
On Wed, Sep 01, 2021 at 08:25:08AM +0000, Nick Gill wrote:
> 
> I'm doing some coding where I process a long list of group presentations. For each presentation I'd like to calculate the order.
> 
> My problem is that I'm not 100% sure if all of the presentations yield finite groups. I'd like to ask GAP to first check to see if the group has order less than a 1000 (say) and, if not, then skip this presentation and move onto the next one.
> 
> My problem is that the Order command seems to ask GAP to give a full coset enumeration and so the loop keeps hanging when it hits possibly infinite groups.
> 
> So... Is there a GAP command that can do a partial coset enumeration to work out lower bounds for the size of a finitely presented group?(Or is there another way around this problem?)

you can use GAP package ACE, which uses an external coset enumeration program ACE,
and pass it option "time=", see
https://www.gap-system.org/Manuals/pkg/ace/htm/CHAP004.htm#SECT017


Probably ACE allows for other ways to terminate coset enumeration early, check the manual.

HTH
Dima