  Let $C(T)$ be a generalized Coxeter group, which has a natural map onto one
of the classical Coxeter groups, either $B_n$ or $D_n$. Let $C_Y(T)$ be a
natural quotient of $C(T)$, and if $C(T)$ is simply-laced (which means all the
relations between the generators has order 2 or 3), $C_Y(T)$ is a generalized
Coxeter group, too . Let $A_{t,n}$ be a group which contains $t$ Abelian groups
generated by $n$ elements. The main result in this paper is that $C_Y(T)$ is
isomorphic to $A_{t,n} \semidirect B_n$ or $A_{t,n} \semidirect D_n$, depends
on whether the signed graph $T$ contains loops or not, or in other words C(T)
is simply-laced or not, and $t$ is the number of the cycles in $T$. This result
extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups
which have a natural map onto one of the classical Coxeter groups.
