We study ℓ-permutation modules of finite general linear groups GL n ( q ) acting on partial flags in the natural module, where the coefficient field of the modules has characteristic ℓ, for ℓ ∤ q . We call the indecomposable summands of these permutation modules linear Young modules. We determine their vertices and Green correspondents, by methods relying only on the representation theory of GL n ( q ) . Furthermore, we show that when the multiplicative order of q modulo ℓ is strictly greater than 1, the Specht modules for GL n ( q ) in characteristic ℓ form a stratifying system. This implies in particular, that for GL n ( q ) -modules with Specht filtration, the filtration multiplicities are independent of the filtration. This is an analogue of a recent theorem by Hemmer and Nakano.