  We ask if any finite type generalized braid group is a subgroup of some
classical Artin braid group. We define a natural map from a given finite type
generalized braid group to a classical braid group and ask if this map is an
injective homomorphism. We prove that this map is a homomorphism for the braid
groups of type A_n, B_n, I_2(k). The injectivity question of this homomorphism
(in these particular cases) is not yet settled. If this map is an injective
homomorphism then several results will follow. For example it will follow that
the Whitehead group, projective class group and the lower K-group of any
subgroup of any finite type generalized braid group vanish. (For the classical
braid group case this vanishing result is proved by the author and F.T. Farrell
in the paper "The Whitehead groups of braid groups vanish".) Also it will
follow that a finite type generalized braid group satisfies Tits alternative
(recently this was asked by M. Bestvina).
