In this paper, we investigate the fixed submodules of modules over skew group rings. We give two applications, the first concerns the determination of a simple basis of the center of a skew group ring. In the second application, we characterize in terms of the structure groups all the mod-retractable skew group rings. More precisely, we prove that if Formula: see text is a group acting on a field Formula: see text with kernel Formula: see text, then the skew group ring Formula: see text is mod-retractable if and only if Formula: see text is mod-retractable and Formula: see text is of finite index in Formula: see text.
Badry et al. (Fri,) studied this question.