Let $R$ be a finite ring with unity and $S$ be an ideal (or subring). Let $R^*$ be the group of units of $R$ and $S^*:=R^* \cap S$. Then does $|S^*|$ divide $|R^*|$ ? Moreover, if $I$ is an ideal of a ring $R$ with unity, then how do to find $(R/I)^*$, i.e. the units of $R/I$ ? And if $S$ is a subring of $R$ containing the ideal $I$, then how to find $(S/I)\cap (R/I)^*$ ?
Please help. Thanks in advance.