2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66695In 1988, Brown and Ellis published [3] a generalised Hopf formula for the higher homology of a group. Although substantially correct, their result lacks one necessary condition. We give here a counterexample to the result without that condition. The main aim of this paper is, however, to generalise this corrected result to derive formulae of Hopf type for the n-fold Cech derived functors of the lower central series functors Z_k. The paper ends with an application to algebraic K-theory.LaTex, 30 pages, uses xypicK-Theory and HomologyCategory Theory18G50, 18G10text