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 local...
