Example GrpCox_BraidGroups (H108E31)

> W<a,b,c> := CoxeterGroup(GrpFPCox, "B3");
> W;
Coxeter group: Finitely presented group on 3 generators
Relations
    a * b * a = b * a * b
    a * c = c * a
    (b * c)^2 = (c * b)^2
    a^2 = Id($)
    b^2 = Id($)
    c^2 = Id($)
> B<x,y,z> := BraidGroup(W);
> B;
Finitely presented group B on 3 generators
Relations
    x * y * x = y * x * y
    x * z = z * x
    (y * z)^2 = (z * y)^2
> P := PureBraidGroup(W);
> P;
Finitely presented group P on 3 generators
Generators as words in group B
    P.1 = x^2
    P.2 = y^2
    P.3 = z^2