Let (R,) be a Noetherian local ring, M a finitely generated R-module with finite projective dimension n, N an arbitrary R-module, and be an ideal of R which is generated by s elements. In this article, we provide a surjective homomorphism from ordinary local cohomology module [image omitted] to top generalized local cohomology module [image omitted], where Pn, M is an nth syzygy of a projective resolution of M. Also, by using this epimorphism, we prove some results about the attached primes, coassociated primes, the Betti numbers, and Artinian properties of certain generalized local cohomology modules. [ABSTRACT FROM AUTHOR]