Gr\'obner bases and some immersion theorems for Grassmann manifolds G_{3,n}

A Gr\"obner basis for the ideal determining mod 2 cohomology of Grassmannian G_{3,n} is obtained. This is used, along with the method of obstruction theory, to establish some new immersion results for these manifolds.
Comment: This is a preprint from 2011. It is already cited in arXiv:1305.0420 [math.AT] as well as in some other already published papers, so we have decided to make it available