Error while calculating automorphism of non abelian group on Gap

Question

I am implementing the following code to calculate the automorphism of non-abelian group on Gap.

f := FreeGroup("b", "c");    # define free group f in two generators
b := f.1; c := f.2;          # call b and c the generators of f
rels := [b^4, (b*c)^2, c^4]; # define relators
G := f/rels;                 # define G

Now, when I run

aut := AutomorphismGroup(G);

to calculate the automorphism group of G, I get the following output and error:

#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
Error, reached the pre-set memory limit
(change it with the -o command line option) in
  prev[2 * limit] := 2 * limit - 1; at /proc/cygdrive/C/gap4r8/lib/grpfp.gi:1201 called from
TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens
 ) at /proc/cygdrive/C/gap4r8/lib/grpfp.gi:1032 called from
CosetTableFromGensAndRels( fgens, grels, List( trial, UnderlyingElement )
 ) at /proc/cygdrive/C/gap4r8/lib/grpfp.gi:3699 called from
Attempt( trial ) at /proc/cygdrive/C/gap4r8/lib/grpfp.gi:3702 called from
Attempt( gens ) at /proc/cygdrive/C/gap4r8/lib/grpfp.gi:3724 called from
FinIndexCyclicSubgroupGenerator( G, infinity ) at /proc/cygdrive/C/gap4r8/lib/grpfp.gi:3773 called from
...  at line 5 of *stdin*
you can 'return;'
brk>

See also a screenshot of this output and error mesage.

Are you using Gap (as in your title and question) or Sage (as in your tag)? Also, could you copy-and-paste the console commands and error message as text rather than linking to a graphic? That makes it easier for us to copy-and-paste sections into our consoles, and also makes it easier for web searches to find this question later. — Rory Daulton, Jun 11 '18 at 14:05
Ashish, you are of course welcome to try this question on SO, but my guess is that specialized questions such as this are probably more profitably referred to the mailing list or other user forum for the particular system you're using, since answering this question requires both more mathematical sophistication than what's common on SO and also some experience with the software. — Robert Dodier, Jun 11 '18 at 16:17
@Ashish are you sure that the defining relations are correct? — Olexandr Konovalov, Jun 19 '18 at 10:20
The permutations b:=(1,2)(3,4,5,6)(7,8,9,10);c:=(1,2,3,4)(5,6,7,8)(9,10); satisfy your relations and generate a group of order 100. — ahulpke, Jun 20 '18 at 10:07

score 3 · Answer 1 · answered Jun 17 '18 at 16:03

What happens is that GAP tries to prove that your group is finite. This fails as your group is infinite.

GAP does not have any method to calculate automorphism groups of arbitrary infinite (finitely presented) groups, in fact I doubt that such an algorithm (can) exist.

The error you get therefore is not a bug, but a feature of the problem you ask.

Your best bet might be to look at the automorphism group of (increasingly larger) characteristic quotients to try to deduce a general pattern of the automorphism group in the hope to prove it later by hand.

Error while calculating automorphism of non abelian group on Gap

1 Answers1