  For modules over group rings we introduce the following numerical parameter.
We say that a module A over a ring R has finite r-generator property if each
f.g. (finitely generated) R-submodule of A can be generated exactly by r
elements and there exists a f.g. R-submodule D of A, which has a minimal
generating subset, consisting exactly of r elements. Let FG be the group
algebra of a finite group G over a field F. In the present paper modules over
the algebra FG having finite generator property are described.
