Possible Duplicate:
$\mathcal{B}_3$ modulo the normal closure of $\mathbb{Z} \times \mathbb{Z} $
What is the index of $\langle (xy)^3,x \rangle$ in the braid group $\mathcal{B}_3 = \langle x,y | xyx = yxy \rangle$ ?
Possible Duplicate:
$\mathcal{B}_3$ modulo the normal closure of $\mathbb{Z} \times \mathbb{Z} $
What is the index of $\langle (xy)^3,x \rangle$ in the braid group $\mathcal{B}_3 = \langle x,y | xyx = yxy \rangle$ ?
I fire GAP and say
gap> f := FreeGroup(2);;
gap> x := f.1;;
gap> y := f.2;;
gap> g := f / [x*y*x*(y*x*y)^(-1)];;
gap> h := Subgroup(g, [(g.1*g.2)^3, g.1]);;
gap> Index(g, h);;
Error, the coset enumeration has defined more than 256000 cosets
called from
TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
TryCosetTableInWholeGroup( H ) called from
CosetTableInWholeGroup( H ) called from
IndexInWholeGroup( H ) called from
...
Entering break read-eval-print loop ...
type 'return;' if you want to continue with a new limit of 512000 cosets,
type 'quit;' if you want to quit the coset enumeration,
type 'maxlimit := 0; return;' in order to continue without a limit
brk>
This suggests that the index is infinite...