Structure of the quotient modules in $hh$ is very complicated. A good understanding of some special examples will shed light on the general picture. This paper studies the so-call $N_{p}$-type quotient modules, namely, quotient modules of the form $h
hominus [z-p]$, where $p (w)$ is a function in the classical Hardy space $H^2(G)$ and $[z-p]$ is the submodule generated by $z-p (w)$. This type of quotient modules serve as good examples in many studies. A notable feature of the $N_{p}$-type quotient module is its close connections with some classical single variable operator theories.
