University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 On one class of modules over group rings with finiteness restrictions 37 46 5087 10.22108/ijgt.2014.5087 EN Olga Dashkova Professor of the Branch of Moscow state university in Sevastopol Journal Article 2014 03 23 The author studies the $\bf R$$G$-module $A$ such that $\bf R$ is an associative ring‎, ‎a group $G$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$C_{G}(A)=1$‎, ‎and for every‎ ‎proper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $A/C_{A}(H)$ is‎ ‎a finite $\bf R$-module‎. ‎It is proved that if the group $G$ under‎ ‎consideration is locally soluble‎ ‎then $G$ is a soluble group and $A/C_{A}(G)$ is a finite $\bf R$-module‎. ‎ https://ijgt.ui.ac.ir/article_5087_ca4189aa5efbaeed67562c6122922f8a.pdf