In this paper we shall give the relationships among $T_R,;End_{R}(M),;SEnd_{R}(M);and;SAut_R(M)$ when M is a perfect R-module. If M and N are perfect modules, we get $SAut_{R}(M { imes}N){cong}SAut_{R}(M){ imes}SAut_R(N)$. Also we shall discuss that $_x(M)_H$ is a subgroup of $_x(M)$ if M is quasi-perfect and $_x(M)_H$ is a normal subgroup of $_x(M)$ if M is perfect.