> < ^ Date: Wed, 21 Apr 1999 11:37:35 +0200 (CET)
> ^ From: Mariano Suarez Alvarez <mariano@fceia.unr.edu.ar >
> ^ Subject: Probably a silly question...

I tried to compute a presentation of the normal closure of
the subgroup generated by the commutator of the two generators of a free
group on two letters with gap, and it appears to be enumerating something
which is infinite.
Below is a transcript of what I tried to do.
This is my very first attempt at using gap, so I very well may be doing
something silly...

Any help will be wellcome.

Thanx,

Mariano Suarez Alvarez

```-----------
```

gap> F := FreeGroup("a",' "b") ;;
gap> E := F / [] ;;
gap> a := E.1 ;; b := E.2 ;;
gap> R := Subgroup( E, [a*b*a^-1*b^-1] ) ;;
gap> PresentationNormalClosure( E, R ) ;
Error, the coset enumeration has defined more than 64000 cosets:
type 'return;' if you want to continue with a new limit of 128000 cosets,
type 'quit;' if you want to quit the coset enumeration,
type 'maxlimit := 0; return;' in order to continue without a limit,
in
CosetTableFpGroup( F, TrivialSubgroup( F ) ) called from
PresentationNormalClosure( E, R ) called from
main loop
brk> return ;
Error, the coset enumeration has defined more than 128000 cosets:
type 'return;' if you want to continue with a new limit of 256000 cosets,
type 'quit;' if you want to quit the coset enumeration,
type 'maxlimit := 0; return;' in order to continue without a limit,
in
CosetTableFpGroup( F, TrivialSubgroup( F ) ) called from
PresentationNormalClosure( E, R ) called from
main loop
brk>
gap>

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