Immersion groups of complex projective spaces

Let M be a closed connected smooth n-dimensional manifold and let R^m be the m-dimensional Euclidean space. Let [M ⊆ R^m] be the set of regular homotopy classes of immersions of M into R^m. If 2m > 3n+1 and there exists an immersion of M into R^m, then the set [M ⊆ R^m] has the structure of an abelian group (see § 1 or [13] ). In this article, we determine the group structure of [CP^n ⊆ R^{4n-i}] for 2≦i≦5, when there exists an immersion of CP^n, the complex projective space of complex dimension n, into R^{4n-i}