A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $ au$ = ($mathbb{T}_ au,;mathbb{F}_ au$) be a hereditary torsion theory such that $mathbb{T}_ au$ $ eq$ Mod-R. Then every $ au$-torsionfree R-module satisfies (P) if and only if S = R/$ au$(R) is a division ring. (2) Let $mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $mathcal{K}$ satisfies (P) if and only if either $mathcal{K}$ = {0} or S = R/$Soc_mathcal{K}$(R) is a division ring, where $Soc_mathcal{K}$(R) = $cap${I 4leq$ $R_R$ : R/I$inmathcal{K}$}.