Abstract: *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).*

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