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I tried with the following code snippet in GAP:

f:=FreeGroup("P","Q");
g:=f/ParseRelators(f, "P^2 = Q^3=1");
Size(g);

But it gets stuck in the following step:

gap> Size(g);
#I  Coset table calculation failed -- trying with bigger table limit
#I  Coset table calculation failed -- trying with bigger table limit
#I  Coset table calculation failed -- trying with bigger table limit
#I  Coset table calculation failed -- trying with bigger table limit

When I terminate the command by Ctrl-C, and then run the last command, the following result is returned:

brk> Size(g);
16384000

Such a simple relationship leads to such a complex group, which makes me a little confused.

Regards, HZ

Hongyi Zhao
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  • This is an infinite group. How do you see `16384000`? If you did not leave the break loop, then `g` may be pointing to something else. – Olexandr Konovalov May 17 '22 at 09:40
  • I added the `brk>` prompt now, which is where I get my results. – Hongyi Zhao May 17 '22 at 09:50
  • While at `brk>` prompt, type `g;` to inspect it. I bet it will be a different `g`, not the group above. – Olexandr Konovalov May 17 '22 at 09:52
  • `g;` will display a lot of digits like `154830, 154831, 154832, 154833, 154834, 154835, 154836, 154837, 154838, 154839, 154840, 154841, 154842, 154843,` – Hongyi Zhao May 17 '22 at 09:54
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    So, it's a list - some intermediate data structure used by the algorithm trying to determine the order of a group. It's infinite, usually repeated "Coset table calculation failed" messages are a sign of that. You need to look at https://www.gap-system.org/Manuals/doc/ref/chap6.html to better understand what to do with GAP break loops. – Olexandr Konovalov May 17 '22 at 09:58

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