  Let $G$ be an arbitrary group such that $G/\Z(G)$ is finite, where $\Z(G)$
denotes the center of the group $G$. Then $\gamma_2(G)$, the commutator
subgroup of $G$, is finite. This result is known as Shur's theorem (the Schur's
theorem). In this short note we provide a quick survey on the converse of
Schur's theorem, generalize known results in this direction and prove the
following result (which is perhaps the most suitable statement for converse of
the Schur's theorem): If $G$ is an arbitrary group with finite $\gamma_2(G)$,
then $G/\Z(G)$ is finite if $\Z_2(G)/\Z(\Z_2(G))$ is finitely generated, where
$\Z_2(G)$ denotes the second center of a group $G$. If $G/\Z(G)$ is finite,
then $\gamma_2(G)$ is also finite and $|G/\Z(G)| \le |\gamma_2(G)|^d$, where
$d$ denotes the number of elements in any minimal generating ser for $G/\Z(G)$.
We classify all nilpotent groups $G$ of class 2 upto isoclinism (in the sense
of P. Hall) such that $|G/\Z(G)| = |\gamma_2(G)|^d$, and ask some questions in
the sequel.
