Olga Dashkova - Professor of the Branch of Moscow state university in Sevastopol

The author studies the \bf RG-module A such that \bf R is an associative ring‎, ‎a group G has infinite section p-rank (or infinite ۰-rank)‎, ‎C_{G}(A)=۱‎, ‎and for every‎ ‎proper subgroup H of infinite section p-rank (or infinite ۰-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. ‎

group ring, linear group, module