On the cohomology ring and upper characteristic rank of Grassmannian of oriented 3-planes

In this paper we study the mod 2 cohomology ring of the Grasmannian G similar to n,3. We determine the degrees of the indecomposable elements in the cohomology ring. We also obtain an almost complete description of the cohomology ring. This description allows us to provide lower and upper bounds on the cup length of G similar to n,3. As another application, we show that the upper characteristic rank of G similar to n,3 equals the characteristic rank of gamma similar to n,3, the oriented tautological bundle over G similar to n,3 if n is at least 8.