  The theory of rough sets was firstly introduced by Pawlak (see \cite{p}).
Many Mathematician has been studied the relations between rough sets and
algebraic systems such as groups, rings and modules. In this paper we will
introduce the lower and upper approximations in a quotient group. We will
discuss several properties of the lower and upper approximations. Moreover
under some additional assumptions we are able to show that the lower
approximation is a normal subgroup of the quotient group but this property
fails for the upper approximation. At the end we will develop several
homomorphisms between lower approximations.
