  We generalize basic results relating the associated graded Lie algebra and
the holonomy Lie algebra from finitely presented, commutator-relators groups to
arbitrary finitely presented groups. In the process, we give an explicit
formula for the cup-product in the cohomology of a finite 2-complex, and an
algorithm for computing the corresponding holonomy Lie algebra, using a Magnus
expansion method. We illustrate our approach with examples drawn from a variety
of group-theoretic and topological contexts, such as link groups, one-relator
groups, and fundamental groups of orientable Seifert fibered manifolds.
