On the mod 2 cohomology algebra of oriented Grassmannians

For n is an element of {2(t)-3, 2(t)-2, 2(t)-1} (t >= 3) we study the cohomology algebra H* ((G) over tilde (n,3); Z(2)) of the Grassmann manifold (G) over tilde (n,3) of oriented 3-dimensional subspaces of R-n. A complete description of H* ((G) over tilde (n,3); Z(2)) is given in the cases n = 2(t) - 3 and n = 2(t) - 2, while in the case n = 2(t) - 1 we obtain a description complete up to a coefficient from Z(2).